{
  "schema": "plectis_lean_experience_graph_v1",
  "authority_posture": "generated_navigation_projection_not_Lean_proof_authority",
  "root_node_id": "universe:plectis-lean",
  "counts": {
    "nodes": 2907,
    "edges": 9145,
    "node_kinds": {
      "human_document": 18,
      "integration_surface": 2,
      "lean_module": 1902,
      "mathematical_object": 105,
      "paper": 22,
      "paper_statement": 689,
      "problem": 8,
      "public_claim": 160,
      "universe": 1
    },
    "relations": {
      "advances_open_target": 40,
      "builds_on": 64,
      "contains": 1909,
      "corollary_of": 1,
      "eliminates_case": 1,
      "explained_by": 22,
      "formalized_in": 43,
      "holds_prepared": 616,
      "imports": 3883,
      "instantiates": 2,
      "interpreted_by": 18,
      "makes_exact": 1,
      "positions": 3,
      "publishes": 160,
      "queued": 24,
      "re_expresses_open_branch": 6,
      "replayed": 616,
      "same_lean_declaration": 92,
      "stated_in_lean": 765,
      "states": 689,
      "supported_by": 190
    }
  },
  "nodes": [
    {
      "id": "claim:actual_foreign_residue_projection",
      "kind": "public_claim",
      "label": "Finite foreign-residue projection reduction",
      "statement": "The finite Möbius residue diagonal splits exactly into projected foreign and divisor channels, and every finite stable tail window has a closed geometric bound. If an analytic kernel/complement bridge controls the actual foreign defect by that bound and the projection is separated from every integer, then the full target is missed. The analytic bridge and any unbounded separated-projection supply are not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:actual_lcm_orbit_nonintegrality_frontier",
      "kind": "public_claim",
      "label": "Actual LCM-orbit non-integrality frontier",
      "statement": "Let H_a = lcm(1,…,2^a) and R_a = totientTail(2H_a) − totientTail(H_a). The totient series S is irrational if and only if, beyond every threshold a₀, some a ≥ a₀ has R_a ∉ ℤ. This is an exact cofinal non-integrality criterion for the actual LCM diagonal. That equivalence itself is not a quantitative separation estimate; the same source also provides a distinct sufficient route in which, cofinally in a₀, some a,q satisfy max 2 a₀ ≤ a, oddGuardedCanonicalAdjacentSuffixDepth (2^a) = 2q+1, and every integer z obeys 1/32 + actualLcmRawErrorRadius a q ≤ |actualLcmTailOrbit a − z|. This quantitative supply is not equivalent to the frontier criterion and remains unproved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:actual_lcm_positive_corridor_top_edge",
      "kind": "public_claim",
      "label": "Actual LCM positive corridor and top-edge boundary",
      "statement": "For a ≥ 8 and J + (a + 6) < 2·2^a, the true translated LCM-orbit difference is strictly positive. If it is represented by an integer and the dyadic modulus has room for the directed endpoint strip, the carry survivor is strictly negative and the discrepancy residue is exactly the top-edge representative 2^K − carry_K, strictly between the strip’s lower edge and 2^K. Thus the positive corridor eliminates the nonnegative true survivor but does not itself produce a central-band contradiction; an independent arithmetic exclusion of the top boundary is still required.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:adelic_height_obstruction",
      "kind": "public_claim",
      "label": "Scalar-localisation height obstruction",
      "statement": "For every rational x, integer c and natural number H, if H divides the reduced denominator of x and the reduced denominator of c·x divides H, then the complementary factor x.den/H divides |c|. Scalar localisation therefore moves that denominator information into the scalar; this local obstruction is not an irrationality criterion.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:adjacent_phase_separation_reduction",
      "kind": "public_claim",
      "label": "Adjacent-pair phase separation reduction",
      "statement": "At scales satisfying the explicit dyadic room inequality, a squared chordal separation of at least 19/25 between two adjacent first-harmonic phases in a dyadic block forces a certified non-integrality witness at one of the two indices. A cofinal supply of such adjacent pairs implies irrationality of the totient constant; no such supply is proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:affine_transport_annihilation",
      "kind": "public_claim",
      "label": "Affine residue state and old-channel annihilation",
      "statement": "The exact Möbius residue kernel has a periodic affine slope-and-intercept state. First-order exponent transport and every coefficient system with vanishing zeroth and first moments annihilate all divisor channels already present at the base height; a prime jump additionally has an explicit migrated-channel correction.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:all_base_totient_kernel_conditional_rank",
      "kind": "public_claim",
      "label": "Conditional exact rank of the all-base totient kernel",
      "statement": "For integers k and e with 2 ≤ k and 1 ≤ e, if the explicit canonical all-base family is linearly independent over ℚ, then the span of the actual all-base totient kernel through level e has dimension k^e + 1. This reusable interface retains the independence input; AllBaseTotientKernel.lean separately discharges it at public checkpoint 25ef6245d15a. As before, this coefficient-space result does not prove irrationality of the binary totient series.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:all_base_totient_kernel_index_reduction",
      "kind": "public_claim",
      "label": "All-base totient-kernel reduction, spanning, and conditional rank",
      "statement": "For every integer base k at least 2, Lean checks the zero-residue scaling identity, the exact nonzero scalar used in composite-base residue reduction, unique quotient/nonzero-digit coordinates, and cardinality k^e + 1 of the canonical finite-level index. It proves unconditionally that this canonical family spans the complete kernel through level e, and proves exact rank k^e + 1 under the explicit hypothesis that the family is linearly independent. Lean does not prove that hypothesis here; the note's evaluation-matrix argument and AllBaseTotientKernel.lean at public checkpoint 25ef6245d15a discharge it by an independent finite-determinant construction, so the unconditional basis and rank theorem takes Martin's positive-density theorem as prior art rather than as an input.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:ani_degree_seven_total_variation_counterexample",
      "kind": "public_claim",
      "label": "Degree-seven Hausdorff-length counterexample",
      "statement": "For ani's explicit monic complex polynomial of degree seven, whose distinct roots lie in the open unit disc, every preconnected subset of the strict unit lemniscate containing two distinct roots has one-dimensional Hausdorff measure greater than 2. In particular, Lean proves the negation and answer(False) forms of the exact Formal Conjectures path-image-length statement. The total-variation bound also remains checked. This formalises one polynomial, not the reported small-parameter family; independent human review of correspondence with the 1958 wording is not recorded.",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:boolean_mobius_carry",
      "kind": "public_claim",
      "label": "Boolean–Möbius carry certificate equivalence",
      "statement": "A nonempty normalised support, one omitting 0, with series value p/q exists exactly when a positive, square-root-bounded integer orbit with Boolean Möbius quotient exists; the support is reconstructed from the certificate.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:boundary_pulse_normalization",
      "kind": "public_claim",
      "label": "Boundary-pulse normalization at the largest-skip crossing",
      "statement": "The row-s pulse of a selected rank e contributes two when e divides 2s+1 and one when e divides 2s+2. For a largest skip d with 2s < 3d, every filled suffix rank d < e < s divides neither index, so the word pulse is exactly the selected-prefix pulse below d. At the first crossing 2s < 3d <= 2(s+1), either 3d = 2s+1 with pulse two or 3d = 2s+2 with pulse one. The transition-carry estimate that would use these exact counts is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:bounded_negative_exclusion",
      "kind": "public_claim",
      "label": "Cofinally bounded negative-magnitude exclusion",
      "statement": "For natural sequences a, C, D, and magnitude and B > 0 satisfying 1 < a(n), C(n) > 0, C(n+1) + D(n) = a(n)·C(n), D(n+1) = a(n)·D(n), bounded rise C(n+1) ≤ C(n) + B, magnitude(n) > 0, division-free normalised vanishing (for every K, eventually K·magnitude(n) < C(n)), and a cofinal negative branch with 0 < e ≤ B and D(t) + e = (a(t)−1)·C(t), the hypotheses are inconsistent. This conditional no-go does not decide the full Erdős #243 endpoint or the mixed-sign and unbounded-negative regimes.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:bounded_rise_fresh_modulus_barrier",
      "kind": "public_claim",
      "label": "Bounded-rise fresh-modulus coprimality barrier",
      "statement": "For natural sequences u and m, if u tends to infinity with upward increments bounded by a fixed positive B, the moduli m are eventually greater than 1 and pairwise coprime, and each earlier m(i) is coprime to every later u(t), then the hypotheses are inconsistent. This is a reusable state-level obstruction, not a proof of the full Erdős #243 assertion.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:calibrated_rational_hankel_countermodel",
      "kind": "public_claim",
      "label": "Rational-value countermodel to a Hankel-signature inference",
      "statement": "An explicit positive atomic moment family and integer formal series have all-rank Hankel order sum_{j<N} j^2 and leading coefficient (N!)^2(N+1)!/2^N, with the same fixed-base asymptotic shape including N^(-8 xi), while xi=G_{2/3}(2/3)=1. For n>=1 the exact reduced moment denominator is 3^(31n+62)(3^(n+1)-2^(n+1))^4; the determinant denominator has logarithmic size Theta(N^3), and a proposed rank-two row-product clearer leaves denominator625. These are ordinary proofs with independent exact finite checks and AI proof reviews, not a Lean proof of the infinite family or human peer review.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": "ordinary_proof",
      "proof_note": "Reviewed ordinary proof; full infinite statement not formalised and independent human review not recorded."
    },
    {
      "id": "claim:campbell_shift_synchronization_boundary",
      "kind": "public_claim",
      "label": "Campbell shift-synchronization strategy boundary",
      "statement": "Campbell's application of the Alford-Granville-Pomerance estimate chooses delta = 1/4, so at prime-search height X the progression modulus d must satisfy d <= X^(1/4), equivalently d^4 <= X. In the proposed last-skip synchronization, P is the fatal-window prime cap, t the unavoidable phase period, and d the combined progression modulus. Taking X = P, the requirements 2 <= d, t <= d, P <= 4t, and d^4 <= P are inconsistent. The shifted-zero interface is guarded by a putative last skip and is exactly equivalent to infinitely many actual greedy skips and to membership of 1/2 in the Mersenne achievement set. It is an endpoint restatement, not an independent Campbell input, and proves no half-membership.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:canonical_jump_slack_reduction",
      "kind": "public_claim",
      "label": "Canonical strict-jump slack reduction",
      "statement": "The two canonical adjacent-suffix central-band inequalities are equivalent to nonnegativity of one explicit integer slack. Cofinal nonnegative slack at strict lcm jumps implies irrationality of the totient constant; that cofinal sign statement remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:certificate_completeness",
      "kind": "public_claim",
      "label": "Certificate completeness",
      "statement": "At fixed parameters, a certified kill exists exactly when the corresponding tail difference is non-integral. At every positive shift, integrality of one tail difference forces S to be rational; thus irrationality is equivalent to pointwise non-integrality, and to pointwise finite certificates.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:certificate_reduction",
      "kind": "public_claim",
      "label": "Exact reduction of #249 to finite decidable certificates",
      "statement": "S is irrational if and only if certified non-integrality witnesses occur at unbounded parameters. The pointwise completeness theorem and the diagonal supply theorem together show that an unbounded lcm-diagonal supply is equivalent as well. Producing that supply remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:certified_kill_instances",
      "kind": "public_claim",
      "label": "Initial certified-kill segment and generated certificates",
      "statement": "Kernel-checked certified kills for the listed small periods, every lcm-diagonal scale t ≤ 82, and the finite certificate shards. The historical 28 explicit deposits through t = 64 form a strict subset of this contiguous finite band.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:channel_quotient_band_breakpoint",
      "kind": "public_claim",
      "label": "Quotient-band channel breakpoint for factorial moments",
      "statement": "For a finite integer coefficient family whose indices all lie in one quotient band k·d ≤ i_j < (k+1)·d, the factorial moment is exactly (d!)^k times the d-channel numerator. In the first band d ≤ i_j < 2d, channel cancellation forces the factorial moment to vanish; with all indices at least d and a nonzero moment, some index is therefore at least 2d.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:coefficient_pencil_finite_rank",
      "kind": "public_claim",
      "label": "Coefficient-pencil positivity and root interlacing through rank eight",
      "statement": "For each real p > 1 and each natural rank N ≤ 8, the coefficient Hankel matrix A_N is positive definite, the polynomial det(Y A_N − B_N) splits over the reals, and every root is strictly below F(p). For adjacent ranks N and N+1 ≤ 8, the ordered root lists interlace non-strictly, with multiplicities. Lean includes N = 0; the paper states the ranks 1 through 8. No all-rank coefficient-pencil theorem, simple-root or strict-interlacing assertion, limiting result, or irrationality of F(3/2) follows from this finite proposition.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:cofinal_cylinder_half_countermodel",
      "kind": "public_claim",
      "label": "Conditional cofinal-cylinder half countermodel",
      "statement": "If for every N there are M,K with max(N,1) ≤ M and a nonempty CylinderStage K M, then an infinite positive support A satisfies ∑_{a∈A} 1/(2^a − 1) = 1/2. This is a conditional countermodel frontier: the cofinal full-cylinder family is not constructed, so neither half-membership nor universal Erdős #257 is settled.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:cofinal_strip_return_closure",
      "kind": "public_claim",
      "label": "Cofinal square-root-strip return closure",
      "statement": "The binary-scaled uncentred greedy half carry is antitone, and the square-root strip envelope divided by 2^N tends to zero. Therefore cofinal returns of the canonical greedy carry to that strip force the scaled carry to tend to zero and yield membership of 1/2 in the Mersenne achievement set. The cofinal return hypothesis is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:composite_dilation_defect_identity",
      "kind": "public_claim",
      "label": "Composite dilation defect identity",
      "statement": "For every positive support element a and positive x, the divisor-count coefficient at a·x is the coefficient at x, plus the distinguished new divisor when a does not divide x, plus an exact finite composite-dilation defect. For a finite-core orthogonal-petal bouquet, the ray defect is bounded by the finite exceptional-frame cardinality plus the petal-support divisor count. This local identity supplies no correlation estimate, tail selector, or irrationality theorem.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:concrete_producer_carry_coordinates",
      "kind": "public_claim",
      "label": "Concrete adjacent-cut producer-carry coordinates",
      "statement": "For every adjacent cut at rank s ≥ 5, the below and above words are the neighbouring subset sums bracketing the target; their remainder and overshoot are the unsigned distances, and their pulses are the paired divisor-incidence contributions of the next two rows. After adjoining terminal rank s, the below producer carry is 4 times the remainder minus the below pulse minus 4, while the above producer carry is the negative of 4 times the overshoot plus the above pulse plus 4. Hence the upper carry is negative and the middle sign depends on the remainder-pulse competition. These exact identities supply no uniform exponential lower bound, sign persistence at unbounded ranks, or universal escape argument.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:concrete_seam_adapter",
      "kind": "public_claim",
      "label": "Concrete finite seam adapter",
      "statement": "Concrete finite seam words realize the abstract adjacent-cut recurrence, and the next seam word agrees with the integer-greedy choice. This implements the finite recurrence but does not establish the unbounded remainder estimate.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:cubic_rate_irrationality_unconditional",
      "kind": "public_claim",
      "label": "Cubic-rate reciprocal-sum irrationality under the stated asymptotic",
      "statement": "For a zero-indexed strictly increasing sequence of positive natural numbers a, if n³(a(n)²/a(n+1) − (1 + 3/n)) tends to zero and the reciprocal series has sum S, then S is irrational. Lean proves the square-specialisation input through the Dedekind-zeta simple pole, so this theorem has no Chebotarev premise. The paper states the ordinary one-based bridge. The quantitative cubic-rate hypothesis is essential here; this does not settle the original eventual Sylvester recurrence assertion.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:cubic_survivor_phase_density",
      "kind": "public_claim",
      "label": "Phase-specific density obstruction for the two cubic survivor profiles",
      "statement": "For either surviving cubic profile Q_{12,c}(n)=2n(n+1)(n+2)+c with c=1 or c=-1, the exact tail recurrences force a mismatch in every sufficiently late four-index window at the corresponding phase modulo 7. The mismatch set therefore has lower density at least 1/7, and hence at least the 1/28 stated in the long paper. No phase-free or arbitrary-profile density statement is claimed.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:denominator_exclusion",
      "kind": "public_claim",
      "label": "Unconditional denominator exclusion for the totient constant",
      "statement": "S = ∑ φ(n)/2ⁿ is not equal to p/q for any integer p and any 1 ≤ q ≤ 79 639 646 646 701 375 323 355 774 875 831 053 (≈ 7.96 × 10³⁴). A lower bound on any rational representation, not a proof of irrationality.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:diagonal_fresh_loss_reduction",
      "kind": "public_claim",
      "label": "Fresh-loss projection and suffix-supply reduction",
      "statement": "The fresh-loss residue certificate is exactly an integer projection inequality, and such a projection forces full-target avoidance. An unbounded projection supply—or the stronger adjacent-suffix gap supplies formalised here—implies irrationality; no unbounded supply is asserted.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:diagonal_pincer_reduction",
      "kind": "public_claim",
      "label": "Exact full-target reduction on the lcm diagonal",
      "statement": "At each lcm-diagonal scale, integrality holds if and only if a foreign-defect term lands in an explicit full-target interval. Globally, S is irrational if and only if the full target is avoided at arbitrarily large diagonal scales; that cofinal avoidance is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:diagonal_pincer_t64_endpoint_certificate",
      "kind": "public_claim",
      "label": "T64 diagonal-pincer endpoint certificate",
      "statement": "Lean checks the diagonal-pincer certified kill at t = 64 using the committed T64 Lucas-primality closure. This is one finite certificate and does not assert an unbounded certificate supply or irrationality.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:diagonal_pincer_t64_primality_closure",
      "kind": "public_claim",
      "label": "T64 diagonal-pincer primality closure",
      "statement": "A generated proof-producing Lucas-certificate module supplies the primality dependencies for the t=47,49,53,59,61,64 diagonal-pincer certificates. This is finite certificate infrastructure; it neither supplies an unbounded certificate family nor proves irrationality.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:dyadic_prefix_block_safety_interfaces",
      "kind": "public_claim",
      "label": "Dyadic-prefix, block-safety, and primitive-overshoot interfaces",
      "statement": "Inside a hypothetical dyadic-rational support value, a reduced finite positive prefix transports exactly to a residual rational support value and wrap-ratio certificate. For the half-greedy orbit, reduced and raw margins, three-depth take-run excess, primitive-lattice cap violation, support-coefficient tail gaps, and gcd-scaled predecessor overshoot are connected by exact identities and equivalences; cofinal supplies of the named witnesses imply that 1/2 belongs to the Mersenne achievement set. Checked fixtures show that safe brackets with numerator monotonicity and a factor-11 predecessor rule are not inductive. No cofinal witness supply is proved, so neither half-membership nor universal Erdős #257 follows.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:dyadic_totient_basis",
      "kind": "public_claim",
      "label": "Explicit basis of the dyadic totient kernel span",
      "statement": "Lean constructs an explicit odd-core-indexed basis of the rational span of the full dyadic totient kernel, with exact span equality and linear independence. This is an independent constructive proof route; its infinite-dimensionality consequence is not an independent contribution because Coons's non-2-regularity theorem already implies it.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:dyadic_totient_certificate_interface",
      "kind": "public_claim",
      "label": "Dyadic totient-kernel finite-level rank",
      "statement": "For every e, a CRT–Dirichlet construction produces a separated nonzero evaluation minor for the canonical dyadic totient-kernel family, which is linearly independent with exact span dimension 2^e + 1. The same Lean development proves that the full dyadic kernel span is not finite-dimensional, but that corollary is not an independent contribution: it is equivalent, for this integer-valued sequence module, to Coons's non-2-regularity theorem. Even residues reduce to odd-core channels, and the compressed-adjoint boundary remains available. These coefficient-side theorems do not prove that S is irrational.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:eb_constant",
      "kind": "public_claim",
      "label": "The Erdős–Borwein constant E is irrational",
      "statement": "E = ∑_{n≥1} 1/(2ⁿ − 1) is irrational, as the base-2 corollary of the full-support theorem.",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:eb_full_support",
      "kind": "public_claim",
      "label": "Full-support Erdős–Borwein irrationality, every integer base b ≥ 2",
      "statement": "For every integer b ≥ 2, the series ∑_{n≥1} 1/(bⁿ − 1) is irrational (Erdős, 1948).",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:erdos_1041",
      "kind": "public_claim",
      "label": "Erdős #1041: short connections inside polynomial lemniscates",
      "statement": "Using ani's explicit monic degree-seven polynomial, Lean proves that every preconnected subset of its strict unit lemniscate containing two distinct roots has one-dimensional Hausdorff measure greater than 2. This refutes the exact Formal Conjectures path-image-length statement and its total-variation counterpart. The reported family is not formalised, and independent human review of correspondence with the 1958 wording is not recorded.",
      "status": "formal statement refuted",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:erdos_1049",
      "kind": "public_claim",
      "label": "Erdős #1049: irrationality of F(t) at rational bases",
      "statement": "For natural numbers 0 < b < a in the Zudilin contour region, Lean proves that F(a/b) is irrational with irrationality exponent at most rationalBaseMeasureBound a b (rational_base_region, rational_base_measure), from the constructed polynomial forms and analytic estimates; in particular F((31/4)^r) is irrational for every positive integer r (thirtyone_four_powers). The universal rational-base assertion remains open; 3/2 lies outside this region and is unresolved here.",
      "status": "open",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:erdos_243",
      "kind": "public_claim",
      "label": "Erdős #243: eventual Sylvester recurrence",
      "statement": "Lean proves that if a is a strictly increasing sequence of positive integers with n^λ(a(n)²/a(n+1) − 1 − λ/n) → 0, then the reciprocal sum ∑ 1/a(n) is irrational, for every non-integer λ > 1, where Lean also derives convergence (nonintegral_regular_rate_irrational), and for λ = 3 whenever the sum converges (cubic_rate_irrationality_unconditional). Both theorems are zero-indexed; the paper transfers them to one-based indexing by an ordinary finite-prefix argument. Without such a rate the eventual Sylvester recurrence assertion remains open: the bounded-rise barrier and the conditional negative-part reductions leave the mixed-sign unbounded regime unresolved.",
      "status": "open",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:erdos_249",
      "kind": "public_claim",
      "label": "Erdős #249: irrationality of S = ∑ φ(n)/2ⁿ",
      "statement": "Lean proves that S = ∑ φ(n)/2ⁿ is irrational if, for every h ≥ 1, there are arbitrarily large X at which the real part of the first-harmonic sum over the good indices is at most 603X/1000 (irrational_totient_series_of_goodBase_gap); the good indices are the assigned indices N in [X, 2X) at the minimal admissible depth with s = 26 whose cofactor m satisfies φ(m) ≥ m/1000. For all large X more than 67X/100 indices are good (eventually_card_pivotGoodBases_gt), and 603/1000 = (9/10)(67/100). Lean also proves that S is irrational if and only if certified non-integrality witnesses occur at unbounded parameters (irrational_totient_series_iff_certificate_supply). The 603X/1000 bound and that unbounded certificate supply are open, so S is not proved irrational.",
      "status": "open",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:erdos_251",
      "kind": "public_claim",
      "label": "Erdős #251: irrationality of Π = ∑_{n≥1} p_n/2ⁿ",
      "statement": "Lean proves that Π = ∑_{n≥1} p_n/2ⁿ equals 2 plus the prime-gap dyadic series and that Π is irrational if and only if that gap series is (tsum_primeDyadicTerm_eq_two_add_primeGap_unconditional, irrational_tsum_primeDyadicTerm_iff_primeGap), with summability from the elementary bound p_n ≤ 1250(n+1)^4; the identity is the known summation by parts. Lean also proves that the consecutive prime gaps are unbounded and not eventually periodic (exists_primeGap0_gt, primeGap0_not_eventually_periodic). The irrationality of Π remains open: these facts do not supply the required cofinal escape for the actual prime gaps.",
      "status": "open",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:erdos_269",
      "kind": "public_claim",
      "label": "Erdős #269: irrationality of running-LCM reciprocal sums",
      "statement": "For every finite set P of at least two primes, the distinct-height sum D_P (each running LCM value of the P-smooth integers counted once) is irrational (res:distinct-height-all; ordinary proof checked by a second AI agent, no human review), as Erdős asserted without an argument in 1973; for |P| = 2 it follows from Hecke-Mahler transcendence, and D_{2,3,5} is Lean-checked (res:distinct-height-235; Comparator not yet run). Each single-prime sub-sum E_p of the catalogue sum is irrational (res:single-prime-subsums; same evidence class as D_P). The catalogue sum for three or more primes is unresolved in this release: for {2,3,5} the rationality-to-positive-reduced-carry bridge is checked, and the remaining endpoint is cofinal local-window escape, equivalently exclusion of the integral branch.",
      "status": "open",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:erdos_68",
      "kind": "public_claim",
      "label": "Erdős #68: irrationality of S = ∑_{n≥2} 1/(n! − 1)",
      "statement": "Lean proves that S = ∑_{n≥2} 1/(n! − 1) is irrational if and only if, for infinitely many m, m does not divide ⌊m!·S_m⌋ + 1, where S_m is the prefix sum through n = m (irrational_factorialGapSeries_iff_cofinal_strictFacTopRat_misses); equivalently, the factorial-gap carry differs from 1 for infinitely many m (irrational_factorialGapSeries_iff_cofinal_nonunit_carries). Lean also proves liminf log L_N/(N^{3/2} log N) ≥ 2√2/3 for the common denominator L_N = lcm_{2≤n≤N}(n! − 1) before cancellation (common_denominator_growth_liminf). The irrationality of S remains open: the checked reductions and finite obstructions do not supply the required cofinal non-unit carries.",
      "status": "open",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:eventually_periodic_negative_no_go",
      "kind": "public_claim",
      "label": "Eventually-periodic negative-orbit exclusion",
      "statement": "For natural sequences a, D, C, and e with 2 ≤ a(n), positive e(N+n) < a(N+n), the exact recurrences D(n+1) = a(n)·D(n) and C(n+1) = C(n) + e(n), the shape equation D(n) + e(n) = (a(n)−1)·C(n), and a positive-period, positive-drift tail e(N+n+h) = e(N+n) and C(N+n+h) = C(N+n) + M with h > 0 and M > 0, the hypotheses are inconsistent. This is only the eventually-periodic negative-magnitude obstruction; mixed-sign and unbounded-negative behaviour remain outside the claim and the full Erdős #243 endpoint remains open.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:fatal_gap_right_tail_classification",
      "kind": "public_claim",
      "label": "Fatal-gap and eventual-right seam classification",
      "statement": "The concrete seam is eventually right when some S >= 5 makes every later seam word append true. A finite prefix u through rank d is a fatal half gap when V(u) + T_(d+1) < 1/2 < V(u) + w_(d+1), which makes every continuation miss 1/2. Eventual rightness is equivalent to the existence of such a gap, to nonmembership of 1/2 in the Mersenne achievement set, and to a final skipped exponent in the real greedy orbit. This exact classification does not decide which branch holds.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:final_middle_cell_escape",
      "kind": "public_claim",
      "label": "Upper and first middle producers cannot feed an all-right tail",
      "statement": "At a putative last false rank D ≥ 13, the upper producer is impossible unconditionally. On the middle branch, let u be the finite support below D and B_D = u union {n : n > D} the lazy support that skips D and selects every later rank. Its value is V(u) + T_D < 1/2, while the exact carry swap sends transition carry C_D to centred carry C_D + 3 at row 2D+1. Thus C_D = -3 gives centred carry zero; the next coefficient rows have at least one and two forced divisors and make the carry negative by row 2D+3, contradicting finite-level nonnegativity below 1/2. This removes the upper branch and one middle cell, not the right-tail branch or the remaining cells -2 and -1.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:final_middle_neg_two_phase_sieve",
      "kind": "public_claim",
      "label": "Rank-26 phase sieve for the final middle -2 cell",
      "statement": "For every seam row s ≥ 27, the greedy decisions through rank 26 select exactly ranks 2, 3, 6, 7, 14, 20, 21, and 26. Consequently, in a hypothetical final middle -2 cell at rank D ≥ 27 followed by an all-right suffix, D mod 21 lies in {11, 14, 17, 20}, D mod 10 is not 8, the mod-10 class 7 cannot pair with the mod-21 class 11, D mod 13 is not 11, and the mod-13 class 10 cannot pair with the mod-21 class 11. Exactly 412 of the 2730 joint residue classes survive. This is a finite necessary condition, not an exclusion; even a later survivor density tending to zero would not suffice without finite extinction or an Archimedean contradiction. The -1 and right-tail branches remain open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:finite_period_noncollapse",
      "kind": "public_claim",
      "label": "Finite-support denominator period noncollapse",
      "statement": "For every finite nonempty support F with 0 ∉ F and integer base b ≥ 2, the reduced denominator of the literal finite sum ∑_{n∈F} 1/(bⁿ−1) is coprime to b and the multiplicative order of b modulo that denominator equals F.lcm id. This finite-support theorem supplies no unbounded support certificate and does not settle the universal infinite-support Erdős #257 endpoint.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:finite_prime_weighted_support",
      "kind": "public_claim",
      "label": "Finite-prime weighted support irrationality",
      "statement": "For every integer base b >= 2, every infinite positive support A with finite weighted mass for some finite nonempty prime set P has irrational support series. If a host H of positive integers has finite base-two weighted mass, then every infinite subset A of H has irrational support series at every integer base b >= 2. This is a sufficient support criterion, not the universal statement.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:first_harmonic_certificate_interface",
      "kind": "public_claim",
      "label": "First-harmonic gap implies a finite certificate",
      "statement": "Under the explicit dyadic room inequality, a constant-saving first-harmonic bound on one block, or on any nonempty finite set of indices below its right endpoint, forces a certified non-integrality witness in that set. No cofinal harmonic estimate is asserted.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:first_harmonic_good_index_reduction",
      "kind": "public_claim",
      "label": "Irrationality of the totient series from one first-harmonic bound on the good indices",
      "statement": "At the minimal admissible depth with s = 26 and η = 1/1000, if for every h ≥ 1 there are arbitrarily large X at which the real part of the first-harmonic sum over the good indices (the assigned indices N in [X, 2X) whose cofactor m satisfies φ(m) ≥ m/1000) is at most 603X/1000, then ∑ φ(n)/2^n is irrational. For all large X more than 67X/100 indices are good, by the unconditional unassigned count and the Chebyshev excluded-cofactor count, and 603/1000 = (9/10)(67/100); the underlying interface asks only for nonempty sets of indices beyond every threshold whose average first cosine is at most 9/10 at a depth with room. The bound is open, sufficient and not known to be necessary. It needs neither the prime number theorem nor a bound on the group means, and it supersedes the prime-number-theorem route at 11X/20. No computation in the record bears on it.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:first_harmonic_pivot_decomposition",
      "kind": "public_claim",
      "label": "Complex first-harmonic pivot decomposition",
      "statement": "For each positive cofactor m at most sqrt(X)/2, the canonical supplier fibre is exactly the injective image of the primes p in the shifted product interval under N = mp - (L-s+1). This exact bijection does not make a supplier prime globally isolated: at X=16, L=20, s=1, m=2, N=18 the pivot is 38=2*19, while the same prime 19 divides the distinct window argument N+1=19. Removing the pivot phase gives an exact decomposition of the block first-harmonic sum into a centred supplier-fibre correlation, a supplier-fibre mean term, a bad-supplier term, and a non-supplier term. At a positive scale satisfying the explicit dyadic-room inequality, if the real part of the centred term is at most 14X/25 and the other three norms are at most X/100, X/100, and 8X/25, then the real first-harmonic sum is at most 9X/10 and yields a finite certificate. A cofinal supply of these budgets implies irrationality of S. No global supplier-prime isolation, prime-distribution estimate, or decorrelation estimate supplying the budgets is proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:fixed_coefficient_rewind_contraction",
      "kind": "public_claim",
      "label": "Fixed-coefficient rewind contraction",
      "statement": "For coefficient c, the canonical inverse parent is T_c(k) = ceil((k+c)/2). For a length-L coefficient list with accumulated offset O, the iterated rewind is R(k) = floor((k+O)/2^L), with phase theta = (1+O) mod 2^L. If 1 <= B <= 2^L, all targets in [1,B] have one ancestor exactly when theta + B - 1 < 2^L; otherwise the endpoint ancestors differ by one and every target maps to one of that adjacent pair. The width bound does not exclude the seam-pair alternative or prove half-membership.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:fixed_precision_transport_no_go",
      "kind": "public_claim",
      "label": "Fixed-precision valuation-unit no-go theorem",
      "statement": "At every fixed positive precision, every finite word of odd valuation-unit symbols admits a compatible carry orbit from an arbitrary incoming integer state, with each successive state within the corresponding valuation-unit radius. Thus bounded local signatures alone cannot exclude all finite centred endpoints; growing precision or global information remains necessary for an endpoint argument.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:fixed_tail_survival_socket",
      "kind": "public_claim",
      "label": "Fixed-tail survival equivalence at every actual skip",
      "statement": "Writing r_M(1/2) for the residual after ranks through M and T_M for the complete tail after M, an actual skip M is final exactly when T_M < r_M(1/2). Negating the existence of a final skip yields r_M(1/2) <= T_M at every actual skip; together with the no-final-skip classification, this is equivalent to membership of 1/2. The required inequalities along the actual greedy orbit are not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:flexible_odd_window_affine_frontier",
      "kind": "public_claim",
      "label": "Affine three-scale frontier for the flexible odd window",
      "statement": "Under the stated short-correction bounds, the three half-word central-band predicates are exactly a three-scale affine escape disjunction. A uniform correction envelope alone cannot force that escape, as a zero-start affine orbit remains inside every scaled edge tube. Thus arithmetic state-correction correlation remains required.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:flexible_odd_window_reduction",
      "kind": "public_claim",
      "label": "Flexible three-rank odd-window reduction",
      "statement": "At an analytically admissible odd power-of-two rank, centrality in any one of the canonical odd rank or its next two base-four successors supplies the existing adjacent-suffix gap interface and hence irrationality. The remaining assertion is a cofinal three-rank band supply; no such supply is proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:fresh_prime_deficit_decomposition",
      "kind": "public_claim",
      "label": "Fresh-prime endpoint-deficit decomposition",
      "statement": "At each positive height, every old-prime endpoint mass dominates the actual totient. The diagonal increment and literal foreign channel split exactly into the old Möbius increment and lower-minus-upper endpoint fresh deficits. The second and five-point curvature operators retain this split, and the nonnegative deficits bound the exact adverse weighted loss from the old-prime curvature margins. No cofinal deficit bound or irrationality conclusion is proved.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:greedy_achievement_geometry",
      "kind": "public_claim",
      "label": "Greedy geometry of the Mersenne achievement set",
      "statement": "The Mersenne achievement set is compact, perfect, totally disconnected, nowhere dense, and has Lebesgue measure one. Membership is equivalent to greedy survival at every level; for the target 1/2 it is exactly equivalent to the canonical greedy orbit omitting infinitely many exponents. No finite normalized support has value 1/2, so positive membership would automatically produce an infinite rational-valued support and refute universal #257. Finite exact-rational death certificates soundly prove non-membership (3/4 is excluded at level one). The strict-tail Cantor geometry is recorded by Kovač–Tao; no novelty claim is made for the formalised refinements.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:half_carry_reachability_compactness",
      "kind": "public_claim",
      "label": "Half-carry reachability and compactness",
      "statement": "At an unresolved even seam, the scalar transition reaches exactly every integer terminal carry other than the one value 2*δ-c. If canonical seam coordinates are supplied at every sufficiently large even depth, then admissible finite half-carry words occur cofinally; compactness yields an infinite support A with erdosSupportSeries 2 A = 1/2. The canonical seam-supply hypothesis is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:half_cylinder_finite_shadow",
      "kind": "public_claim",
      "label": "Finite shadows of the half cylinder",
      "statement": "For an admissible depth-N half-carry word with support A, terminal carry K_N, and future tail T_N, the residual is exactly 1/2 - X_A = (K_N - T_N)/2^N. At a first even seam the sole missing carry is H = 2 delta - c, so the integer strip [1,B] is fully reachable exactly when H lies outside it. The rank-three fixture A = {2,3} has residual 1/42 < 1/32 but its depth-six strip [1,8] contains H = 3, so raw dyadic safety does not force seam escape. The sole conditional membership input is the unproved governed frozen-margin producer, which requires future coefficient rows to cover the centred carry within J <= k+1 after every skipped rank k+1.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:half_divisor_unit_drop",
      "kind": "public_claim",
      "label": "Half-divisor unit coefficient drop at the feedback row",
      "statement": "At the doubled feedback row, switching only the terminal half-divisor bit from false to true changes the support coefficient from C to C+1 and, under K' = 2K-C, drops the successor carry by exactly one. The same identity holds for any explicitly identified adjacent boundary pair, and the rewind adapter transfers such a shared-cutoff pair to the next protected seam while retaining the unit-drop witness. This does not construct such pairs globally.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:half_greedy_two_thirds_band",
      "kind": "public_claim",
      "label": "Exact band localization of the final skip between two takes",
      "statement": "Suppose a take at rank b is followed by the next take at c > b+1, put q = 2^b − 1 and m = 2^(c−1), and write the pre-take residual as 1/R with 0 < R < q. The final intervening skip is dyadically unsafe exactly when q(m−1)/(q+m−1) < R < qm/(q+m), an interval of exact width q^2/((q+m)(q+m−1)). For one intervening skip this specializes to the two-thirds band (q(2q+1)/(3q+1), 2q(q+1)/(3q+2)), whose width is below 1/9; integral reciprocals never lie there, and the corresponding positive odd numerator is at least 7. These are local constraints: no theorem here says that the actual greedy orbit for 1/2 avoids a band or identifies the surviving last-producer cells with unsafe skips.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:half_membership_seam_classification",
      "kind": "public_claim",
      "label": "Positive half-membership classification in seam coordinates",
      "statement": "Membership of 1/2 in the Mersenne achievement set is equivalent to false successor terminal bits beyond every bound, to a cofinal sequence of such bits, and to a cofinal integer-seam sequence whose skipped ranks tend to infinity. These equivalences do not establish that any positive producer exists.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:half_second_channel_reduction",
      "kind": "public_claim",
      "label": "Exact rational second-channel reduction for the target one half",
      "statement": "A decidable rational separation predicate controls the greedy Mersenne orbit for the target 1/2. Lean verifies levels 1 through 6 exactly; proving the predicate for every n >= 7 would place 1/2 in the Mersenne achievement set, equivalently would force infinitely many canonical greedy skips. The universal tail statement remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:half_trapping_return_carry_interface",
      "kind": "public_claim",
      "label": "Half-trapping reverse-carry interface",
      "statement": "Scalar-relation-invariant rational-linear channels have no nontrivial square determinant at any rank. Separately, a common coefficient word with a 1/0 seam and a common following overlap forces the terminal reverse-carry difference to be a power of two times an odd integer; a common nonnegative real carry bound yields the corresponding dyadic spacing inequality. The module neither supplies reverse-carry presentations nor a predecessor overlap, so it is not a greedy separation or irrationality theorem.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:independent_clock_channel_relations",
      "kind": "public_claim",
      "label": "Complete rational relations for integer-radix independent-clock sums",
      "statement": "For positive rationally independent clock rates with no simultaneous positive crossings, and integer radices b_i >= 2, all rational relations among 1 and the channel sums S_i are multiples of (-1,b_1-1,...,b_d-1). The proof uses genuine late swaps with a common infinite suffix in one orbit closure, a fixed rational lattice, and density of the clock section. The explicit rates 1,sqrt(2),sqrt(3),sqrt(6) and radices 2,3,5,7 give rational span dimension four. This is an ordinary proof reviewed by AI agents, without Lean or independent human verification of the infinite theorem.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": "ordinary_proof",
      "proof_note": "Reviewed ordinary proof; full infinite statement not formalised and independent human review not recorded."
    },
    {
      "id": "claim:integer_greedy_first_wrap_reduction",
      "kind": "public_claim",
      "label": "Integer-greedy first-wrap reduction",
      "statement": "For every s >= 3, let C_s = 2^(2s-1) - 2^s, let B_s = 2 floor(sqrt(2s)) + 4, and let r_s be the remainder obtained by greedily subtracting each descending truncated seam weight from C_s whenever possible. Each weight exceeds its complete tail by at least 2^(s+1) > B_s. Hence a positive subset-sum defect at most B_s exists exactly when 1 <= r_s <= B_s. The downstream skipped-seam escape hypothesis requires B_s < r_s at every genuine skipped rank. That hypothesis is not proved, so Erdős #257 remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:largest_skip_gap_propagation",
      "kind": "public_claim",
      "label": "Largest skipped-rank gap and successor propagation",
      "statement": "At row s, let d be the largest skipped rank, u the selected prefix below d, L the integer weight of u together with the filled suffix above d, and U the weight obtained by replacing that suffix with d. In the late range d > 2s/3, equivalently 2s < 3d, Lean proves 3L + (3*2^(s+1) + 2*4^(s-d) + 4) = 3U. Upper or middle successors make the new terminal rank s the largest skip, while right successors preserve d. The global statement forcing an upper or middle step when 2(s+1) < 3d first fails is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:largest_skip_induction_reduction",
      "kind": "public_claim",
      "label": "Largest-skip induction from a quantified first-crossing hypothesis",
      "statement": "Assume that for every s >= 14 and largest skip d with 2s < 3d, either 2(s+1) < 3d or the transition to row s+1 is upper or middle. Lean checks the base s = 14, d = 13 with 28 < 39. Under the hypothesis, induction gives a largest skip beyond two thirds at every row s >= 14; these skipped ranks tend to infinity, so 1/2 belongs to the Mersenne achievement set. The universal next-row hypothesis is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:last_producer_tail_escape_reduction",
      "kind": "public_claim",
      "label": "Last-producer tail-escape reduction",
      "statement": "If every actual middle transition at D ≥ 13 other than the discharged cell C_D = -3 satisfies Theta_D < C_D, then an eventual right seam is impossible and 1/2 belongs to the Mersenne achievement set. Since Theta_D ≥ 0, this leaves two open inputs: exclude C_D = -2,-1 and prove Theta_D < C_D at every remaining transition with C_D ≥ 0. A square-root producer lower bound is a separate sufficient hypothesis. None of these arithmetic inputs is proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:lcm_factor_ideal_anchor_pulse_no_go",
      "kind": "public_claim",
      "label": "LCM factor-ideal anchor-pulse no-go theorem",
      "statement": "For every t ≥ 3, a nonzero synthetic affine carry has forcing letters in the principal ideal generated by φ(lcm(1,…,t)), matches every stated whole-ray anchor, and remains within the diagonal bounds while its state is a strict survivor. The same countermodel survives every finite integer shift polynomial. Thus factor ideals, whole-ray anchors, and finite-rank shift algebra alone do not force carry escape. The construction does not assert that its forcing letters are actual totient differences and does not rule out nonlinear use of fresh divisor channels.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:localized_protected_seam_compactness",
      "kind": "public_claim",
      "label": "Localized protected seam compactness",
      "statement": "At depth M, realized localized seam means only the forward implication: every seam-reachable carry k in [3,27] is the terminal carry of an admissible finite word. The seam's unique hole is H = 2 delta - c, so choosing k = 4 when H = 3 and k = 3 otherwise supplies one admissible word. If such realizations occur cofinally, then cofinal admissibility and an infinite support A with erdosSupportSeries 2 A = 1/2 follow. The cofinal realization supply is not proved, so Erdős #257 remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:mersenne_lambert_ladder",
      "kind": "public_claim",
      "label": "The Mersenne–Lambert ladder identities",
      "statement": "L(μ) = 1/2, L(φ) = 2, L(φ*μ) = S, and the Möbius-square lens S = 1/2 + ∑ μ(d)/(2^d − 1)², placing the open constant one convolution from the machine-checked irrational E.",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:mersenne_shadow_denominator",
      "kind": "public_claim",
      "label": "Exact Mersenne-shadow denominator and survivor bounds",
      "statement": "The reduced denominator of the lcm-height scaled Möbius shadow is computed exactly at every height, and for t ≥ 5 an explicit upper-half Mersenne product both divides it and supplies a quantitative lower bound.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:mersenne_tail_atom_boundary",
      "kind": "public_claim",
      "label": "Finite Mersenne tail-atom determinant boundary",
      "statement": "A periodic Mersenne tail atom has the exact doubling-and-wrap carry law. For any finite atom matrix, clearing the product of its column Mersenne denominators yields the integral numerator determinant; a nonzero cleared weighted minor therefore has absolute value at least one. This is a finite-denominator boundary for an atom-minor route, not an irrationality criterion for S.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:middle_producer_cardinality_reduction",
      "kind": "public_claim",
      "label": "Finite-prefix middle-producer cardinality reduction",
      "statement": "Put g_D = #G_D. The augmented finite support A_D = G_D union {D} has g_D + 1 elements, so its complete future divisor-incidence tail satisfies Theta_D ≤ g_D + 1. Since C_D = 4 R_(D,D) - P_D - 4, the inequality g_D + P_D + 5 < 4 R_(D,D) is exactly g_D + 1 < C_D; required at every late middle transition, it excludes the negative cells and proves tail dominance, hence half-membership. The stronger row-scale hypothesis R_(D,D) ≥ D also suffices. Neither hypothesis is proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:mixed_cofinal_half_carry_fan_in",
      "kind": "public_claim",
      "label": "Mixed cofinal half-carry fan-in",
      "statement": "For every N, suppose there is M >= N carrying either a selected protected half-carry window or a localized realized one-hole seam. The window branch chooses carry 1; the seam branch chooses 4 when its unique hole is 3 and 3 otherwise. Either branch supplies one admissible finite word, and the branches may alternate with N. Hence cofinal admissibility and, by compactness, an infinite support A with erdosSupportSeries 2 A = 1/2 follow. This mixed cofinal hypothesis is not proved, so Erdős #257 remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:mixed_prime_power_layer_identity",
      "kind": "public_claim",
      "label": "Mixed prime-power support-layer identity",
      "statement": "Exact p-adic and q-adic coefficient-layer operators commute. For distinct primes and a residual argument coprime to their product, the two-layer operator on the support coefficient equals the iterated exact-prime-power pullback. The checked singleton {12} fixture has mixed (2²,3) layer value one at residual argument one. This is finite coefficient algebra only, with no decimation transport, bounded-Ω endpoint, or irrationality theorem.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:mixed_weighted_cover_support",
      "kind": "public_claim",
      "label": "Mixed weighted and positive-cover support irrationality",
      "statement": "Let E have finite base-two finite-prime weighted mass and let V lie in a strengthened positive-cover host. Every infinite support A contained in E union V has irrational support series at every integer base b >= 2. The theorem uses a common observation scale; it does not assume separate irrationality conclusions for the two components.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:mobius_sign_support_no_go",
      "kind": "public_claim",
      "label": "Möbius-sign support one-half no-go",
      "statement": "The Boolean support selected by the negative Möbius values has sum 1/2 plus the positive Möbius tail and is therefore at least 1/2 + 1/63. This closes the sign-truncation route to the target value 1/2; it does not exclude another infinite Boolean support with that value.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:newton_ray_separation_consumer",
      "kind": "public_claim",
      "label": "Finite Newton-flow ray separation and perturbation consumer",
      "statement": "An explicit exponential-decay Newton connection can occur only when its endpoint values lie on the same positive ray; conversely, every finite injective complex family admits an arbitrarily small common translation making all values nonzero and all positive-ray arguments distinct. These are finite perturbative and conditional connection statements.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:nonintegral_regular_rate_irrationality",
      "kind": "public_claim",
      "label": "Nonintegral regular-rate reciprocal-sum irrationality",
      "statement": "For a zero-indexed strictly increasing sequence of positive natural numbers a and a real noninteger lambda greater than one, if n^lambda (a(n)^2/a(n+1) - (1 + lambda/n)) tends to zero, then the reciprocal series converges and its sum is irrational. The Lean theorem derives summability from the rate; the one-based paper form uses an ordinary finite-prefix bridge. The little-o remainder is essential to the integer-extraction argument. This does not settle the unrestricted Erdős #243 problem.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:orthogonal_petal_sunflower_reduction",
      "kind": "public_claim",
      "label": "Conditional orthogonal-petal sunflower reduction",
      "statement": "For a finite-core orthogonal-petal bouquet at base 2, the exact uniform tail-selection predicate implies a forced-carry certificate supply and hence irrationality of the associated support series. Lean formalises the carry conversion and an explicit infinite alternating-core, squared-prime-petal bouquet whose elements have three prime factors with multiplicity. The tail-selection predicate itself is not proved, so this does not add an unconditional #257 support family.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:parity_socket_obstruction",
      "kind": "public_claim",
      "label": "Parity obstruction for the reduced margin socket",
      "statement": "For every positive even modulus and every radius in the stated nontrivial range, each parity class contains both a reduced-margin-socket hit and a miss. The same holds for a positive power-of-two modulus. Thus quotient parity alone cannot decide the reduced signed-margin socket. No t = 827 numeral or signed-margin certificate is asserted.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:period_four_signed_residue_obstruction",
      "kind": "public_claim",
      "label": "Period-four signed residue-selection obstruction",
      "statement": "For the period-four signed weight 1,0,−1,0, the associated signed divisor coefficient vanishes for every n congruent to 3 modulo 4. A whole arithmetic progression can therefore carry zero coefficient, so residue-blind selection cannot force a protected nonzero residue for every periodic signed weight.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:periodic_nonnegative_weight_irrationality",
      "kind": "public_claim",
      "label": "Eventually-periodic nonnegative weighted Lambert irrationality",
      "statement": "For every integer base b ≥ 2, an eventually-periodic nonnegative rational coefficient sequence with a positive value at a positive index in its periodic region has irrational series ∑ γ(a)/(b^a − 1). This includes eventually-periodic natural-number weights and indicator supports. Luca–Tachiya prove a broader periodic rational-coefficient theorem by different methods; no priority claim is made here.",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:periodic_signed_weight_dichotomy",
      "kind": "public_claim",
      "label": "Periodic signed-weight irrational-or-terminating dichotomy",
      "statement": "For every integer base b ≥ 2 and every periodic integer weight w, the signed series ∑ w(a)/(b^a − 1) is irrational or some power of b times its value is an integer. Excluding that terminating alternative implies irrationality. The terminating alternative is not excluded in general, so the full mixed-sign periodic-coefficient theorem is not claimed.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:pivot_anti_reconstruction_reduction",
      "kind": "public_claim",
      "label": "Pivot anti-reconstruction and window-pair reduction",
      "statement": "On a finite supplier fibre, sufficient counted phase-pair separation feeds a certified non-integrality witness through exact reconstruction-defect and variance identities. Cofinal pivot anti-reconstruction, reconstruction variance, or counted-pair producers imply irrationality of S. The fibre-free cofinal window-pair predicate is exactly equivalent to irrationality of S. No cofinal arithmetic producer is proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:power_two_bit_lift",
      "kind": "public_claim",
      "label": "Exact power-of-two one-bit lift",
      "statement": "Given agreement modulo 2^k, agreement modulo 2^(k+1) is exactly evenness of the signed quotient after division by 2^k; failure gives the unique offset class. In particular, a signed difference 16*c agrees modulo 32 exactly when c is even. Under the stated correction and margin budget, the centered signed-margin socket is exactly failure of this next lift. This provides a finite fifth-bit interface and does not supply cofactor parity at unbounded scales.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:prime_gap_identity_tao",
      "kind": "public_claim",
      "label": "Tao's already-known prime-to-gap identity",
      "statement": "Tao posted the prime-to-gap identity by summation by parts (erdosproblems.com/251, 7 October 2025). That identity is already-known mathematics, not a theorem of this checkout, and is not the public lead; the supported lead is the coefficient-only countermodel and sparse rationalising perturbation.",
      "status": "cited only",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:prime_gap_irrationality_equivalence",
      "kind": "public_claim",
      "label": "Exact prime-gap dyadic irrationality equivalence",
      "statement": "Lean checks that the prime-value dyadic series is irrational exactly when the prime-gap dyadic series is. The named iff still takes a Summable hypothesis; this checkout discharges that hypothesis by the elementary bound p_n ≤ 1250(n+1)^4 (not the prime-number theorem) and the unconditional identity. Neither side is proved irrational. This formalises known summation-by-parts; the public attribution of that identity is the cited-only row prime_gap_identity_tao.",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:prime_gap_unboundedness_and_nonperiodicity",
      "kind": "public_claim",
      "label": "Unbounded and non-eventually-periodic consecutive prime gaps",
      "statement": "The consecutive-prime-gap sequence is unbounded and is not eventually periodic with any positive period. These coefficient facts do not by themselves imply irrationality of the prime-gap or prime-index dyadic series.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:prime_support_irrationality",
      "kind": "public_claim",
      "label": "Irrationality of the prime-support series ∑_p 1/(2^p − 1)",
      "statement": "Tao–Teräväinen; settles the prime-support special case of #257. Only the identity bridge to ∑ ω(n)/2ⁿ is formalised, not the irrationality.",
      "status": "cited only",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:primitive_coordinate_index_obstruction",
      "kind": "public_claim",
      "label": "Primitive Euler-coordinate finite-jet obstruction",
      "statement": "For the primitive-conductor weight A = φ*μ, every positive index clearing the normalized coordinates A(n)/n through horizon N is divisible by the two-tier primorial: 4 at the prime 2 once N ≥ 4, p² for odd p with p² ≤ N, and p otherwise. Hence no fixed positive index clears all normalized coordinates. This is a finite Euler/Witt-coordinate obstruction only; it gives no irrationality criterion for S.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:primitive_unit_gap_ceiling",
      "kind": "public_claim",
      "label": "Prime-power reduced-denominator unit-gap ceiling",
      "statement": "For the reduced-denominator unit-gap predicate at an odd prime power p^e, the candidate interval is empty or has exactly one candidate divisible by p; in particular its count is at most one. The exact row (u,N,K) = (3,3,5) satisfies the unit-gap predicate while the corresponding ordinary empty-gap inequality fails. This is a finite certificate-level strengthening, not an unbounded supply theorem or an irrationality criterion for S.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:producer_carry_future_tail_socket",
      "kind": "public_claim",
      "label": "Exact producer-carry residual and sign criteria",
      "statement": "For A contained in {2,...,d}, let f_A(n) count support divisors, let C_(A,d) be the affine integer state after 2d+1 updates from 1, and let Theta_(A,d) be the complete scaled coefficient tail after depth 2d+2. Then 1/2 - X_A = 2^(-(2d+2))(C_(A,d) - Theta_(A,d)). Hence C_(A,d) > Theta_(A,d) iff X_A < 1/2 and C_(A,d) < Theta_(A,d) iff X_A > 1/2; a negative carry is sufficient for the latter because the tail is nonnegative, and carry at most -8 gives a full Mersenne-gap margin. No occurrence theorem for these carries is proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:quarter_band_endpoint_cells",
      "kind": "public_claim",
      "label": "Exact quarter-band failure cells for adjacent seam cuts",
      "statement": "At row s put H = 2^(s-1), and let R, U, R', p^-, p^+ be the adjacent cut's remainder, overshoot, next remainder, below pulse, and above pulse. On the non-carry middle branch, failure R' >= 8H is equivalent to the unique cell R = H+k with p^- <= 4k < p^-+4. On the terminal-reset branch, failure is equivalent to R = 3H+k with p^-+4 <= 4k and 4k+16H < 4(R+U)+p^+. These are exact failure classifications, not an avoidance theorem for the concrete seam orbit.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:rational_base_cleared_tail_recurrence",
      "kind": "public_claim",
      "label": "Exact rational-base cleared-tail recurrence",
      "statement": "For rational r, s, B, and F, a coefficient sequence coeff : ℕ → ℚ, and r ≠ 0, the denominator-cleared tail state satisfies rationalBaseClearedTailQ (r, s, B, F, coeff) (N + 1) = r · rationalBaseClearedTailQ (r, s, B, F, coeff) N − B · coeff (N + 1) · s^(N + 1) for every N. The identity is not derived from rationality and is not itself a rationality contradiction.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:rational_base_forcing_growth",
      "kind": "public_claim",
      "label": "Rational-base forcing-term growth boundary",
      "statement": "For natural s, B, coeff, and N, if s ≥ 2, B ≥ 1, and coeff(N + 1) ≥ 1, then rationalBaseForcingNat s B coeff N ≥ 2^(N + 1); at s = 1 the same quantity is exactly B · coeff(N + 1). This is an elementary forcing-term bound, not a bounded-state contradiction or endpoint result.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:realized_rewind_phase_identity",
      "kind": "public_claim",
      "label": "Realized rewind phase identity",
      "statement": "For a realized carry-one fixed-coefficient history, list the suffix bits newest row first and let X be their binary numeral, so the newest bit has weight 2^0. If D = 2^L, the rewind phase is exactly theta = D - 1 - X. The interval [1,B] rewinds to one ancestor exactly when B - 1 <= X; equivalently, for the frozen-prefix carry Z = 1 + X, exactly when B <= Z. No theorem proves either coverage inequality at all sufficiently large depths.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:reciprocal_mass_bound",
      "kind": "public_claim",
      "label": "Rationality-forced reciprocal-mass lower bound",
      "statement": "A rational support-series value with odd denominator part v forces reciprocal mass at least 1/ord_v(2), or divergence; an infinite support with dyadic-rational value has reciprocal mass divergent or greater than one.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:reciprocal_summable_support",
      "kind": "public_claim",
      "label": "Reciprocal-summable support irrationality at every integer base",
      "statement": "For every integer base b >= 2 and every infinite support A, summability of the reciprocal-support mass implies that the support series is irrational. No pairwise-coprimality hypothesis is required. Erdős (1968) stated this extension without proof.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:reset_deficit_escape_geometry",
      "kind": "public_claim",
      "label": "Exact right-branch window and reset-deficit escape law",
      "statement": "Write R_s for the final integer-greedy remainder and p_s^- for the below pulse. At a largest skip d with 2s < 3d, a right branch forces 2^(s+1)+4 <= 4R_s and 12R_s+3*2^(s+1) < 4*(3*2^(s+1)+2*4^(s-d)+4)+6(s-2), and it satisfies R_(s+1)+2^(s+1)+p_s^-+4 = 4R_s. If R_s <= 2^s and delta_s = 2^s-R_s, every further right step gives delta_(s+1) >= 4 delta_s while the reference scale doubles; hence 2^s <= 2^k delta_s forces an upper-or-middle row t in [s,s+k]. The global anti-concentration needed to exclude the pinned interval along the actual orbit is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:residual_gauge_obstruction",
      "kind": "public_claim",
      "label": "Residual-gauge obstruction for monomial minors",
      "statement": "For a residual-weighted monomial matrix, common nonzero residual weights act by a right diagonal gauge and preserve determinant nonvanishing. Under the locked inverse-phase gauge, an exponent-one row is identically 1 even when the determinant remains nonzero; allowing row-dependent residuals reconstructs a consecutive-power matrix with zeroth row identically 1. Thus residual-blind rank, determinant, and conditioning criteria alone cannot exclude the target. This does not rule out a criterion with an additional arithmetic coupling identity, and it gives no irrationality criterion.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:rewind_boundary_pair_obstruction",
      "kind": "public_claim",
      "label": "Finite rewind boundary-pair obstruction",
      "statement": "A concrete depth-26 selected two-word window has a depth-27 explicit rewind step with history [1], a width-two numerical seam, and the doubled-row identity, but no depth-13 half-divisor boundary-pair witness. Therefore scalar one-row seam data alone does not entail the structural boundary predicate required by the cofinal consumer.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:rewind_seam_operational_bridge",
      "kind": "public_claim",
      "label": "Operational bridge from rewind seams to protected next-row seams",
      "statement": "Let W = (a^h)_(1 <= h <= R) be a selected depth-N window whose targets rewind to two adjacent base words at depth M. If D and phi are the rewind denominator and phase, delta = D-phi, M <= N, (N+1)/2 <= M, R <= D, and the adjacent base words have row-(N+1) coefficients c+1 and c, then f_(a^h)(N+1) equals c+1 for h <= delta and c for h > delta. If 27 <= S <= 2 floor(sqrt(N+1))+4 and S+c+1 <= 2R, the profile realizes a protected one-hole seam at row N+1. The rewind provenance, seam pair, coefficient drop, strip, and buffer are inputs. For a full half-strip window the divisor bound supplies the buffer, but the coefficient drop remains unproved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:seam_producer_carry_alignment",
      "kind": "public_claim",
      "label": "Exact seam-hole to producer-carry alignment identity",
      "statement": "Let P omit s, put A = P union {s}, and let delta be the half-carry of A at row 2s-2. Define the first-wrap hole H = 2 delta - f_P(2s) and paired incidence pulse Pi = 2 f_A(2s+1) + f_A(2s+2). Then the producer carry is exactly C(A,s) = 4(H-1) - Pi. This aligns the seam and producer coordinates but supplies no sign, size, or occurrence estimate.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:selected_half_carry_window_compactness",
      "kind": "public_claim",
      "label": "Selected half-carry windows",
      "statement": "A selected half-carry window at depth N and radius R assigns every k in [1,R] an admissible Boolean word of depth N whose terminal carry is k. If such windows exist at every sufficiently large depth with R >= 1, their k = 1 representatives give cofinal finite admissibility; compactness then yields an infinite support A with erdosSupportSeries 2 A = 1/2. The unproved object-level input is a coherent one-row history: either all representatives agree on membership of every divisor of N+1, making their next coefficient common, or the adjacent outcome realizes the canonical one-hole seam. The module supplies no such cofinal history.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:selected_staircase_integral_height_boundary",
      "kind": "public_claim",
      "label": "Smith index and primitive one-target border boundary",
      "statement": "The selected staircase matrix with ones on and below the diagonal and integer r>=2 above it has Smith factors 1,r-1,...,r-1. For the selected {2,3,5} kernel, any entrywise-integral diagonal clearing has determinant magnitude at least 4^(N-1), whereas the reduced rational determinant has numerator one up to sign. A rational single-target border has primitive polynomial plus or minus (tX-s), where s/t is the reduced Schur complement. These ordinary arithmetic arguments were reviewed by AI agents; they are not the existing Lean nonvanishing theorem and have no independent human review.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": "ordinary_proof",
      "proof_note": "Reviewed ordinary proof; full infinite statement not formalised and independent human review not recorded."
    },
    {
      "id": "claim:selected_suffix_cylinder_propagation",
      "kind": "public_claim",
      "label": "Conditional suffix-cylinder feedback and child-gap recurrence",
      "statement": "For the depth-18 selected window, the common depth-13 prefix and suffix numeral satisfy ν + k = 17. Under a common next coefficient C the endpoint obeys E' = 2E - C. At a feedback row the full cylinder either advances or leaves one carry gap [g_-,g_+]. If the lower and upper families have coefficients C_- and C_+ and satisfy the explicit positivity, ordering, strip, and buffer inequalities, the next gap is exactly [2g_- - C_- - 1, 2g_+ - C_+]. Cutoff promotion appends forced bits 0 and 1 and preserves consecutive prefixes. A swallowed two-row update forces the sharp quarter-band bound B <= 4(g_+ - g_- + 1) + 2. Cofinal full stages would produce an infinite support of value 1/2, but no such cofinal family or uniform coefficient inequalities are proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:selected_suffix_pre_feedback_run",
      "kind": "public_claim",
      "label": "Verified finite suffix-cylinder stages through depth 52",
      "statement": "A common depth-13 prefix supports full selected windows at every depth 18 through 27, and the threshold continuation reaches depth 29 while covering the protected strip. At depth 29, cutoffs 14 through 25 remain common and cutoff 26 does not. A separate exact recurrence reaches depth 51 with endpoint 51,327,745 beyond the next head threshold, and the promoted depth-52 successor supplies a terminal-strip witness. These are finite stages, not an unbounded induction.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:selected_window_depth18_base",
      "kind": "public_claim",
      "label": "Computed depth-18 selected half-carry window base",
      "statement": "A kernel-reflected Boolean table supplies a selected half-carry window at depth 18 for every terminal carry in the half strip [1,12]. The representatives share a common depth-13 restriction, yielding the first next-row divisor-agreement certificate. This is a finite base and does not construct selected windows at unbounded depths.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:separated_cut_algebraic_lambert_transcendence",
      "kind": "public_claim",
      "label": "Algebraic-base transcendence on separated divisibility supports",
      "statement": "For an infinite positive-integer host with cuts L_j < M_j, L_j tending to infinity and M_j-L_j tending to infinity, every host exponent at most L_j dividing L_j and every later exponent divisible by M_j, every infinite thinning with bounded positive integer weights has transcendental Lambert sum at every real algebraic base t > 1. This includes all divisibility chains and an explicit host of unbounded divisibility width and divergent reciprocal sum. The full number-field Subspace Theorem argument has two AI proof reviews; it is an ordinary proof with no Lean transcendence theorem, independent human review or asserted historical priority.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": "ordinary_proof",
      "proof_note": "Reviewed ordinary proof; full infinite statement not formalised and independent human review not recorded."
    },
    {
      "id": "claim:sigma_transcendence",
      "kind": "public_claim",
      "label": "Transcendence of ∑ σ(m)/2^m",
      "statement": "Nesterenko (1996); the ladder rung L(Id). Cited for positioning, not formalised here.",
      "status": "cited only",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:signed_dyadic_moment_substrate",
      "kind": "public_claim",
      "label": "Signed dyadic-moment algebra",
      "statement": "A rectangular determinant expansion over all maps and a unique-largest-dyadic-exponent parity lemma are formalised. The latter makes a cleared finite dyadic sum odd, hence nonzero, when its selected numerator is odd and its exponent is strictly largest. This is finite algebraic substrate only: it proves neither non-vanishing of the actual totient Hankel determinants nor an irrationality criterion.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:signed_totient_entire_defect_interpolation",
      "kind": "public_claim",
      "label": "Arbitrarily slow signed interpolation preserving Dirichlet singularities",
      "statement": "For any integer beta>=2 and positive allowance f(n) tending to infinity, an interval around the totient value is filled by integer sequences b=phi+e with 0<=b(n)<=n and |e(n)|<=f(n). One target-independent even support has upper Banach density zero, leaving any fixed prefix and odd coefficients unchanged. The construction preserves every fixed eventual coefficient and cumulative congruence, gives eventually constant progression moment defects outside common hulls of density zero, entire progression Dirichlet defects, and smooth root-of-unity radial germs with prescribed finite zero jets. The full proof includes the allowance-dependent block bound and first-harmonic rational countermodels. It is an ordinary proof with two AI proof reviews, not a Lean proof of the infinite theorem or independent human review.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": "ordinary_proof",
      "proof_note": "Reviewed ordinary proof; full infinite statement not formalised and independent human review not recorded."
    },
    {
      "id": "claim:square_crt_correction_suppression",
      "kind": "public_claim",
      "label": "Square-CRT correction suppression",
      "statement": "For every finite family of distinct primes and prescribed anchors, a bounded simultaneous square-CRT base removes the prime-dilation correction at every admissible finite shift. Checked clean cubes can have vanishing coefficients and can also have a nonzero coefficient; this finite mechanism supplies neither an unbounded certificate family nor an irrationality criterion for the totient constant.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:squared_lambert_gcd_moments",
      "kind": "public_claim",
      "label": "Squared-Lambert identities for divisor count and the first gcd moment",
      "statement": "The squared-Mersenne Lambert series with weight 1 equals the base-1/2 series of sigma(n)-tau(n), and the series with weight phi equals the base-1/2 series of P(n)-n, where P is Pillai's gcd-sum function. These are the exact divisor-count and first-moment identities for the fair-coin gcd law; the separately cited irrationality of the constant-weight value is not claimed as formalised here.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:squared_mersenne_enclosure",
      "kind": "public_claim",
      "label": "Sharp squared-Mersenne diagonal enclosure",
      "statement": "The scaled diagonal tail difference is written as an explicit Lambert-projected centre plus a signed squared-Mersenne tail, with a sharp symmetric bound and a checked separation criterion for missing the full target.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:squarefree_support_irrationality",
      "kind": "public_claim",
      "label": "Irrationality of squarefree-support series at power-of-two bases",
      "statement": "Duverney–Tachiya Corollary 1.2 and Example 1.1 prove linear independence of 1 and the squarefree Lambert sums at bases 2^j (j≥1), including n=1; subtracting each rational n=1 term settles the support {n≥2:n squarefree} at every power-of-two base. Their condition |q|L≤s, with L=lcm(1,…,ℓ), here permits q=2 but does not cover integer bases that are not powers of two. This result is not formalised here.",
      "status": "cited only",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:stern_brocot_cylinder_law",
      "kind": "public_claim",
      "label": "Reduced-direction normalization and Stern–Brocot cylinder law",
      "statement": "The Mersenne weights of positive reduced slopes sum exactly to one. At every positive Stern–Brocot node (a,b), the cylinder mass 1/((2^a-1)(2^b-1)) splits into its stop mass and two child cylinders; the depth-d unfolding has error between zero and (2/3)^d times the cylinder mass and converges to the closed form.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:stern_brocot_run_fibonacci_stability",
      "kind": "public_claim",
      "label": "Fibonacci and continuant stability of Stern–Brocot runs",
      "statement": "A Stern–Brocot word with r nonempty alternating runs has height at least F_(r+3), with equality on the all-unit run spine. Writing each run length as 1+e_i gives an exact multiaffine continuant-defect expansion, the sharp global gain F_(r+1) sum e_i, and exact one-site coefficient F_(i+2)F_(r-i+1). Under the gcd-one weight 2^-(a+b), the first induced run layer has mass 1/2, while the natural denominator-bookkeeping exponent is exactly F_(r+3)-2. These are source-level combinatorial and arithmetic facts; no analytic denominator survival or irrationality conclusion is claimed.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:strengthened_positive_cover_support",
      "kind": "public_claim",
      "label": "Strengthened positive-cover support irrationality",
      "statement": "A strengthened positive divisor-cover datum with summable scaled cost makes every infinite subset of its host irrational at every integer base b >= 2. The statement retains the nonlinear cover majorant and summability hypotheses; it does not cover arbitrary supports.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:strict_prime_tail_orbit_gap",
      "kind": "public_claim",
      "label": "Tail-orbit phase-density and natural-prime strict-gap reductions",
      "statement": "A uniform 11/100 nonpositive-phase density on arbitrarily late dyadic blocks yields an 89/100 first-harmonic saving and hence a finite certificate; alternatively, cofinally many natural prime indices with tail-orbit real part below 9/10 yield adaptive pivot escape. The exact initial phase is the scaled-angle character of (2^h - 1) times the series, and the tail phase follows a power-of-two squaring orbit from it; phase 1 is equivalent to an integral actual tail difference, while an entered dyadic root obstructs the strict-gap producer.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:sublog_zero_windows",
      "kind": "public_claim",
      "label": "Sublogarithmic divisor-coverage zero windows",
      "statement": "A rational support-series value forces every zero window in the divisor-count coefficient to have length at most ε·log₂(N+1) + B, where B ≥ 0 is built from ε, c and v but is bound after the support and numerator, so no single constant is claimed uniform across supports. This constrains coverage; it does not solve universal #257.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:support_families",
      "kind": "public_claim",
      "label": "Named infinite-support irrationality families toward #257",
      "statement": "For every base b ≥ 2, ∑_{n∈A} 1/(bⁿ − 1) is irrational for factorial support, power-of-two support, multiples, pairwise-coprime supports with summable reciprocals, eventually-periodic supports, residue classes, and the odd numbers. Proved families, not the universal statement.",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:tail_orbit_rigidity",
      "kind": "public_claim",
      "label": "Tempered tail-orbit rigidity criterion",
      "statement": "For coefficients c(n) ≤ n, the binary series ∑ c(n)/2ⁿ is rational exactly when a tempered integer carry orbit exists, and every tempered orbit equals the scaled tail.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:terminal_only_cofinal_closure",
      "kind": "public_claim",
      "label": "Terminal-only cofinal square-root-strip closure",
      "statement": "A normalized finite word with terminal half carry in the square-root strip has support-series value within (4M+12)/2^M of 1/2. Thus cofinally many such terminal-only witnesses, with neither coherent histories nor earlier-row bounds, force 1/2 into the Mersenne achievement set and yield an infinite support with support-series value 1/2. The cofinal terminal-witness supply is not proved.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:terminal_scaled_vanishing_closure",
      "kind": "public_claim",
      "label": "Scaled terminal-vanishing closure",
      "statement": "A normalized sequence of finite terminal words whose depths tend to infinity and whose terminal carries divided by the corresponding powers of 2 tend to zero has support-series values converging to 1/2. Closedness of the Mersenne achievement set then gives membership of 1/2 and an infinite support with that value. The prior cofinal square-root-strip condition maps into this weaker socket, but no scaled-vanishing sequence is constructed.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:terminal_scaled_vanishing_half_countermodel",
      "kind": "public_claim",
      "label": "Conditional terminal-scaled-vanishing half countermodel",
      "statement": "Any HalfTerminalOnlyScaledVanishingSequence—finite words avoiding ranks 0 and 1, depths tending to infinity, and terminal carry divided by 2^M tending to zero—produces an infinite support A with ∑_{a∈A} 1/(2^a − 1) = 1/2. Hence that antecedent would refute universal Erdős #257, but it is not constructed here and does not itself settle half-membership.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:three_halves_coordinatewise_corridor_no_go",
      "kind": "public_claim",
      "label": "Base 3/2 coordinatewise corridor exclusion",
      "statement": "With N ≥ 1 and K ≥ 1, the six-condition CoordinatewiseCorridor at base 3/2 is impossible for every natural Q and digit. This excludes only that literal coordinatewise clearing architecture, not rationality or irrationality of F(3/2) or any other proof architecture.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:three_prime_bounded_certificate_safety",
      "kind": "public_claim",
      "label": "Size-authenticated bounded certificate checks for #269",
      "statement": "The bounded width and cumulative-array checkers expose their size hypotheses, are sound on every accessed entry, compose across adjacent ranges, and carry explicit regressions showing that default-zero array access, half-height cancellation, and finite coverage cannot certify an infinite/cofinal conclusion. No paper numerical table is executed or validated by these safety theorems alone.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:three_prime_cofinal_window_carry_extinction",
      "kind": "public_claim",
      "label": "Conditional cofinal-window extinction of bounded carries for #269",
      "statement": "If the denominator-dependent cofinal local-window residue escape holds, then for every positive multiplier B coprime to 30 there is no positive integral sequence satisfying the exact cleared recurrence d_{n+1}=b_n d_n−B m_n together with the corresponding short bound. The same contradiction applies to an explicitly absorbed nonzero common-factor carry after exact cancellation. For the actual {2,3,5} series, the rationality-to-positive-reduced-carry bridge is established separately; the cofinal escape producer remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:three_prime_exact_modulus_pinning",
      "kind": "public_claim",
      "label": "Exact-modulus pinning for an actual #269 window",
      "statement": "If an actual finite {2,3,5} window has a least-positive forcing residue no larger than the exact carry cap, then the scaled normalized launch lies within that cap divided by the actual window modulus of an integer. Irrationality plus a separately supplied exact-modulus decay estimate therefore yields cofinal local-window escape. The decay estimate and irrationality input are not proved by this claim.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:three_prime_finite_prefix_completion_boundary",
      "kind": "public_claim",
      "label": "Finite #269 radix prefixes admit an altered rational completion",
      "statement": "Every finite positive integral radix prefix with nonnegative integral digits extends to a positive rational orbit by changing the future to radix 2 and digit 1. In particular, the actual word through any finite horizon has such an abstract completion. This is a countermodel to finite-prefix-only inference and is not a rational model of the actual infinite smooth-number series.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:three_prime_finite_residue_contradiction",
      "kind": "public_claim",
      "label": "Finite least-positive-residue contradiction for #269",
      "statement": "For a positive modulus C, a positive integer state c bounded by K cannot be congruent to x modulo C when the canonical least-positive representative of x is greater than K; the zero residue class is represented by C. The integer carry form and exact residue classifier are checked in Lean.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:three_prime_octic_window_equivalence",
      "kind": "public_claim",
      "label": "Conditional o(8^a) equivalence band for #269",
      "statement": "For a cap G which dominates the long-paper cap for every positive denominator and satisfies G(B,n)/8^n -> 0 for each positive B, cofinal local-window escape is equivalent to irrationality of the three-prime paper series. Both the dominance and little-o hypotheses are explicit; the theorem proves neither side unconditionally.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_carry_kernel_anti_compression",
      "kind": "public_claim",
      "label": "Totient carry anti-compression",
      "statement": "If the binary totient coefficient series were rational, one positive-multiplier tempered integral carry would have uniformly eventually-periodic dyadic sections modulo its multiplier while retaining canonical carry-section span dimension at least 2^e − 1 for every e. No finite-rank bound for every rationality-supplied carry is proved, so this quotient-periodicity/anti-compression conjunction is a necessary consequence rather than an irrationality criterion for S.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_coprimality_probability",
      "kind": "public_claim",
      "label": "Fair-coin coprimality form of the totient constant",
      "statement": "For independent fair-coin geometric waiting times X and Y on the positive integers, S = 1/2 + P(gcd(X,Y)=1), where the probability is the visible coprime-pair series. That probability has no rational representation with denominator at most 39819823323350687661677887437915526. This is an exact reformulation and quantitative corollary; irrationality remains open.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_residue_series_classification",
      "kind": "public_claim",
      "label": "Irrational totient residue series and the rational dyadic residue observables",
      "statement": "For every m ≥ 3 the series ∑_{n≥1} (φ(n) mod m)/2^n is irrational, and for k ≥ 1 and f: Z/2^kZ → Q the series ∑_{n≥1} f(φ(n) mod 2^k)/2^n is rational exactly when f is constant on the even residue classes, with value 3f(1)/4 + c/4 where c is that constant. The first assertion, in every integer base, already follows from Erdős's Lemma 1 (Indag. Math. 19 (1957), p. 213; the case b = 0 of his Lemma 4, pp. 215-218) because φ(n) mod m vanishes outside a set of density zero, and equally from Theorem 3 of Kaneko, Suzuki and Tachiya (arXiv:2601.20743v1, p. 5). Those criteria also give the classification when the values f(r) - f(0) on the even classes have one sign; with both signs they need a further spacing hypothesis, which the isolated-coefficient proof does not need. Wong posted the case in which the base equals the modulus in 2015. No novelty claim is made for the first assertion. The reduced series say nothing about the unreduced series ∑ φ(n)/2^n.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_residue_series_dilations",
      "kind": "public_claim",
      "label": "Linear independence of dilated totient residue series",
      "statement": "For every integer t ≥ 2 and m ≥ 3, the numbers 1 and ∑_{n≥1} (φ(n) mod m)/t^{dn}, d = 1, 2, ..., are linearly independent over Q. For a finite set D of positive integers and residue functions f_d: Z/2^{k_d}Z → Q with k_d ≥ 1, any rational constant plus ∑_{d∈D} ∑_{n≥1} f_d(φ(n) mod 2^{k_d})/t^{dn} is rational exactly when every f_d is constant on the even residue classes. The proof isolates a nonzero coefficient at the least active dilation by the Chinese remainder theorem and Dirichlet's theorem. When all coefficients of a relation have one sign, Erdős's Lemma 1 (1957) already excludes it; the mixed-sign case is not covered by that criterion without a further spacing hypothesis.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_residue_series_integer_radix",
      "kind": "public_claim",
      "label": "Totient residue series in every integer base",
      "statement": "For every integer t ≥ 2 and m ≥ 3 the series ∑_{n≥1} (φ(n) mod m)/t^n is irrational, and for k ≥ 1 and f: Z/2^kZ → Q the series ∑_{n≥1} f(φ(n) mod 2^k)/t^n is rational exactly when f is constant on the even residue classes, with value (t+1)f(1)/t^2 + f(0)/(t^2(t-1)). The first assertion already follows from Erdős's Lemma 1 (1957) and from Theorem 3 of Kaneko, Suzuki and Tachiya, as recorded for the binary case; no novelty claim is made for it.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_v8_conditional_peripheral_assembly",
      "kind": "public_claim",
      "label": "Conditional peripheral-and-centred assembly for the #249 first-harmonic route",
      "statement": "Under eventual peripheral estimates and a cofinal centered estimate at one shared depth function, the exact finite decomposition supplies the first-harmonic gap consumer and hence the conditional irrationality route. Both analytic suppliers remain explicit hypotheses; no unconditional Erdős #249 conclusion follows.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_v8_finite_arithmetic_threshold",
      "kind": "public_claim",
      "label": "Exact finite arithmetic and run-threshold checks for #249",
      "statement": "The four displayed discrepancy values at (h,X,L)=(1,4,9), their finite room and certified kills, the Farey denominator bound, and the corrected finite run threshold hold exactly. These finite facts do not supply a cofinal certificate producer.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_v8_generic_centering_countermodel",
      "kind": "public_claim",
      "label": "Generic centering countermodel for the #249 decomposition",
      "statement": "A two-point complex model has vanishing peripheral mean contributions while its centered contribution remains nonzero. This refutes the generic inference from peripheral cancellation to a centered budget; it is not a counterexample to the arithmetic totient-centered predicate.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_v8_one_finite_first_harmonic_instance",
      "kind": "public_claim",
      "label": "One unconditional finite first-harmonic gap instance",
      "statement": "At (h,X,L)=(1,4,9), the exact finite first-harmonic expression has the certified norm gap bounded by 21X/25. This is one finite instance and does not establish DTWFirstHarmonicNormGap or any cofinal statement.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:totient_v8_peripheral_finite_budget_bridge",
      "kind": "public_claim",
      "label": "Finite peripheral estimates assemble into PivotBudgetAt",
      "statement": "Exact phase, residual, cardinality, and uniform fibre-mean estimates compose into PivotBudgetAt. The bridge proves neither the prime-distribution estimates nor the centered estimate required by the endpoint route.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:transport_certificate_instances",
      "kind": "public_claim",
      "label": "Verified transport-window certificates",
      "statement": "Lean verifies the sharp prime-jump certificate at (H,p,L)=(12,5,15) and the balanced three-transport certificate at (H,L)=(60,12). These bounded instances do not establish any unbounded supply.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:transport_curvature_reductions",
      "kind": "public_claim",
      "label": "Transport and curvature reductions for Erdős #249",
      "statement": "Curvature, fixed-three exponent transport, anchored (3,5) transport, prime-jump, and balanced three-transport observables each have exact finite non-integrality consumers whose unbounded supply would imply irrationality of the totient constant. Every supply hypothesis remains open.",
      "status": "conditional reduction",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:twenty_one_quotient_greedy_frontier",
      "kind": "public_claim",
      "label": "Canonical quotient-greedy and scaled-remainder frontier at 1/21",
      "statement": "Membership of 1/21 in the Mersenne achievement set is equivalent both to excluding one explicit fatal/cofinite/aligned branch and to cofinally bounded scaled actual greedy remainders. Every closed Boolean quotient row is the deterministic quotient-greedy row; any unbounded sequence of canonical rows with remainder at most 2^R gives membership. On the complementary fatal branch the remainder is eventually strictly supercapacity, the boundary rank is always selected, and support and remainder follow one exact affine recurrence. A final skipped exponent also forces a structured one-sided approximation to the Erdős–Borwein constant with exact denominator-order constraints. These results isolate permanent affine supercapacity as the surviving late regime; they do not contradict it or prove 1/21 membership.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:unbounded_carry_states",
      "kind": "public_claim",
      "label": "Carry states are unbounded over infinite rational-valued supports",
      "statement": "An infinite support with rational series value has an unbounded positive carry state, closing finite-state readings of the carry system.",
      "status": "proved here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:universal_257",
      "kind": "public_claim",
      "label": "Erdős #257, universal form",
      "statement": "Lean proves that for every integer base b ≥ 2 and every finite nonempty set P of primes, with h(a) the largest divisor of a supported on P, every infinite set A of positive integers with ∑_{a∈A} h(a)/(a(b^{h(a)} − 1)) finite has ∑_{n∈A} 1/(bⁿ − 1) irrational (divisibilityWeightedClaim). Lean also proves irrationality at every such base for every infinite A with ∑_{a∈A} 1/a finite (irrational_erdosSupportSeries_of_summable_reciprocal), and exhibits sets with divergent reciprocal sum all of whose infinite subsets have irrational series at every such base (finite_monotone_witness_rule_realised). Irrationality of ∑_{n∈A} 1/(2ⁿ − 1) for every infinite A remains open.",
      "status": "open",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:upper_reset_band_certificates_through_thirty",
      "kind": "public_claim",
      "label": "Upper-reset dyadic-band certificates through row 30",
      "statement": "At an upper transition G_(d+1) = H_d, put Q_d = 4 O_d + A_d from the upper overshoot and divisor pulse and B_(d,j) = 2^(d-j+1). For every 13 <= d <= 30 and j <= d, Lean proves B_(d,j) < Q_d or Q_d + 2(d+j) <= B_(d,j), equivalently avoidance of Q_d <= B_(d,j) < Q_d + 2(d+j). For fixed d, one exact successor remainder R_(d+1,d+1) certifies every j. This is bounded evidence and proves no global upper-reset band-escape hypothesis.",
      "status": "verified finite instance",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:van_assche_qapery_diagonal_no_go",
      "kind": "public_claim",
      "label": "Van Assche q-Apéry diagonal recurrence non-transfer",
      "statement": "For every real p > 1, the n = 0 residual obtained by applying the Amdeberhan–Zeilberger q-Apéry operator to Van Assche's moving diagonal is the displayed strictly negative factorisation, hence is nonzero. This rules out that selected diagonal for that recurrence at n = 0; it proves no general recurrence, endpoint, or #1049 irrationality result.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:weighted_phase_carry_finite_observer",
      "kind": "public_claim",
      "label": "Weighted-phase carry split and finite realised span for #269",
      "statement": "The exact weighted-phase carry recurrence splits into a finite residue digit, each of the two coordinates staying inside its declared interval, and an integral quotient coboundary that is not controlled. An explicit factorisation through a finite-dimensional function-faithful observer then forces the realised symbolic span to be finite. Nothing here proves a finite-state quotient or a literal infinite realised span, and no rationality or irrationality conclusion follows.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:zudilin_all_rank_hankel_order",
      "kind": "public_claim",
      "label": "All-rank normalized Hankel order and leading coefficient",
      "statement": "For every natural N, including N = 0, the normalized Zudilin Hankel determinant has q-order N(N-1)(2N-1)/6. Its leading coefficient satisfies the division-free identity 2^N times the coefficient = (N!)^2 (N+1)!, with the corresponding rational quotient formula. The all-row producer is proved rather than assumed. This algebraic theorem does not by itself supply the analytic estimates or irrationality at 3/2. Zudilin (2016) proves the q-order inequality; the equality is proved here.",
      "status": "unconditional progress",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "claim:zudilin_rational_base_region",
      "kind": "public_claim",
      "label": "Zudilin rational-base irrationality and irrationality-exponent bound",
      "statement": "For natural numbers 0 < b < a satisfying ZudilinContourRegion a b, the Lambert value F(a/b) is irrational and its irrationality exponent is at most rationalBaseMeasureBound a b. The proof constructs the polynomial forms and proves their clearing, nonvanishing and asymptotic estimates. In particular, F((31/4)^r) is irrational for every positive natural r. These are formalizations of the stated Zudilin region and its consequences, not universal rational-base irrationality; 3/2 is outside the region.",
      "status": "formalised here",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/claims.json",
      "proof_status": null,
      "proof_note": null
    },
    {
      "id": "document:architecture",
      "kind": "human_document",
      "label": "Repository architecture",
      "role": "system_explanation",
      "href": "documents/architecture.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/ARCHITECTURE.md"
    },
    {
      "id": "document:comparator-1049",
      "kind": "human_document",
      "label": "Comparator #1049 fixture",
      "role": "comparator_case_study",
      "href": "documents/comparator-1049.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/verification/COMPARATOR_1049_NUMERICAL_HEIGHT.md"
    },
    {
      "id": "document:documentation",
      "kind": "human_document",
      "label": "Documentation guide",
      "role": "documentation_index",
      "href": "documents/documentation.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/README.md"
    },
    {
      "id": "document:external-verification",
      "kind": "human_document",
      "label": "External verification",
      "role": "comparator_explanation",
      "href": "documents/external-verification.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/EXTERNAL_VERIFICATION.md"
    },
    {
      "id": "document:formal-conjectures",
      "kind": "human_document",
      "label": "Formal Conjectures contributions",
      "role": "upstream_contribution_record",
      "href": "documents/formal-conjectures.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/verification/FORMAL_CONJECTURES_CROSSWALK.md"
    },
    {
      "id": "document:methodology",
      "kind": "human_document",
      "label": "Methodology",
      "role": "evidence_method",
      "href": "documents/methodology.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/METHODOLOGY.md"
    },
    {
      "id": "document:orientation",
      "kind": "human_document",
      "label": "Technical orientation",
      "role": "generated_reader_map",
      "href": "documents/orientation.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/ORIENTATION.md"
    },
    {
      "id": "document:paper-guide",
      "kind": "human_document",
      "label": "Current papers",
      "role": "current_paper_catalogue",
      "href": "documents/paper-guide.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/README.md"
    },
    {
      "id": "document:prior-art",
      "kind": "human_document",
      "label": "Prior art",
      "role": "attribution_and_antecedents",
      "href": "documents/prior-art.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/PRIOR_ART.md"
    },
    {
      "id": "document:reading-guide",
      "kind": "human_document",
      "label": "A reader's way in",
      "role": "reader_introduction",
      "href": "documents/reading-guide.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/READING_GUIDE.md"
    },
    {
      "id": "document:readme",
      "kind": "human_document",
      "label": "Repository overview",
      "role": "human_front_door",
      "href": "documents/readme.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/README.md"
    },
    {
      "id": "document:related-problems",
      "kind": "human_document",
      "label": "Related problems",
      "role": "portfolio_relationship_map",
      "href": "documents/related-problems.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/RELATED_PROBLEMS.md"
    },
    {
      "id": "document:residual-progress",
      "kind": "human_document",
      "label": "Residual progress",
      "role": "open_boundary_progress",
      "href": "documents/residual-progress.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/reference/RESIDUAL_PROGRESS.md"
    },
    {
      "id": "document:results",
      "kind": "human_document",
      "label": "Results and open boundaries",
      "role": "mathematical_results_map",
      "href": "documents/results.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/RESULTS.md"
    },
    {
      "id": "document:scope",
      "kind": "human_document",
      "label": "Scope and claim boundary",
      "role": "scope_boundary",
      "href": "documents/scope.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/SCOPE.md"
    },
    {
      "id": "document:source-map",
      "kind": "human_document",
      "label": "Source map",
      "role": "proof_and_exposition_crosswalk",
      "href": "documents/source-map.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/SOURCE_MAP.md"
    },
    {
      "id": "document:wave-index",
      "kind": "human_document",
      "label": "Development index",
      "role": "development_chronology",
      "href": "documents/wave-index.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/reference/WAVE_INDEX.md"
    },
    {
      "id": "document:weighted-257-task",
      "kind": "human_document",
      "label": "Apply a result and change a hypothesis",
      "role": "changed_hypothesis_task",
      "href": "documents/weighted-257-task.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/reading-edition/weighted-257-task.md"
    },
    {
      "id": "integration:comparator",
      "kind": "integration_surface",
      "label": "Comparator",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/EXTERNAL_VERIFICATION.md"
    },
    {
      "id": "integration:palomar",
      "kind": "integration_surface",
      "label": "Palomar",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/docs/verification/PALOMAR_QUALIFICATION.md",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/verification/PALOMAR_QUALIFICATION.md",
      "registry_status": {
        "schema": "plectis_palomar_registry_status_v1",
        "observed_at": "2026-10-09T15:50:27.855436+00:00",
        "entries": [
          {
            "entry": "PalomarCorpus_E257_01",
            "title": "Weighted support criteria for reciprocal Mersenne subseries",
            "problem_ids": [
              "erdos_257"
            ],
            "repository": "wcook04/plectis-erdos-lean",
            "commit": "b85ed30805188eb4390a686b111294b24363418e",
            "comparator_config_path": "PalomarCorpus/E257_01/comparator.json",
            "formalization_metadata_path": "PalomarCorpus/E257_01/formalization.yaml",
            "theorem_names": [
              "PalomarCorpus.E257.DivisibilityWeightedSupport.divisibilityWeightedClaim",
              "PalomarCorpus.E257.MixedWeightedCover.mixedSupportClaim",
              "PalomarCorpus.E257.PaperStructuresBO.arbitraryWeightMixedSupport_allBase_hereditary",
              "PalomarCorpus.E257.VariableExponentCover.strengthenedPositiveCoverClaim",
              "PalomarCorpus.E257.WeightedCloseReturn.weighted_displacement_cofinal_close_return"
            ],
            "status": "registered",
            "observed_at": "2026-10-09T14:42:56Z",
            "registered_url": "https://palomar-registry.org/entry.html?id=PALOMAR-2026-09-25-000009&version=1",
            "verification_run_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/36009433226",
            "observation_basis": "public_registry_and_authenticated_status"
          },
          {
            "entry": "ExternalVerification269ThreePrimeStructure",
            "title": "Erdős #269 — three-prime structure",
            "problem_ids": [
              "erdos_269"
            ],
            "repository": "wcook04/plectis-erdos-lean",
            "commit": "c39cea6a976747d132a848d26f110b9c608d5a45",
            "comparator_config_path": "ExternalVerification269ThreePrimeStructure/comparator.json",
            "formalization_metadata_path": "ExternalVerification269ThreePrimeStructure/formalization.yaml",
            "theorem_names": [
              "Erdos249257.ExternalVerification269ThreePrimeStructure.smoothPrefixLcm_eq_threePrimeHeight",
              "Erdos249257.ExternalVerification269ThreePrimeStructure.threePrimeKernelQ_eq_of_sameLogCell",
              "Erdos249257.ExternalVerification269ThreePrimeStructure.threePrimePositiveJumpSet_card",
              "Erdos249257.ExternalVerification269ThreePrimeStructure.finiteSmoothKernelSum_groupedByHeight",
              "Erdos249257.ExternalVerification269ThreePrimeStructure.smoothExponentShell_card_quadratic",
              "Erdos249257.ExternalVerification269ThreePrimeStructure.kernel_235_minor_eq_neg_one_fifteen",
              "Erdos249257.ExternalVerification269ThreePrimeStructure.threePrimeKernel_infiniteRank_and_noFiniteSeparation"
            ],
            "status": "registration_requested",
            "observed_at": "2026-10-09T15:33:02Z",
            "registered_url": null,
            "verification_run_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/35190946875",
            "observation_basis": "maintainer_authenticated_status",
            "publication_blocker": {
              "reason": "unsupported_lean_version",
              "summary": "The publication renderer rejected the reviewed Lean 4.29.0 source because its current minimum is Lean 4.35.0-rc2. Palomar must repair rendering and retry this registration; sending consent again does not resume it.",
              "evidence_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/37948913697",
              "observed_at": "2026-10-09T15:33:02Z"
            }
          },
          {
            "entry": "PalomarCorpus_E257",
            "title": "Erdős #257 — September corpus edition",
            "problem_ids": [
              "erdos_257"
            ],
            "repository": "wcook04/plectis-erdos-lean",
            "commit": "52f29ad173b04e3bac941b3663f2b9aebe5de0bb",
            "comparator_config_path": "PalomarCorpus/E257/comparator.json",
            "formalization_metadata_path": "PalomarCorpus/E257/formalization.yaml",
            "theorem_names": [
              "PalomarCorpus.E257.AchievementSetGeometry.supportedMersenneAchievementSet_geometry_and_volume",
              "PalomarCorpus.E257.AchievementSetGeometry.volume_supportedMersenneAchievementSet_eq_zero_of_rat_value",
              "PalomarCorpus.E257.ActualUpperSuccessor.actualUpperRightPacketLinearEscape_iff_successorLinearEscape",
              "PalomarCorpus.E257.ActualUpperSuccessor.actualUpperSuccessorLinearEscape_completeCounterexample",
              "PalomarCorpus.E257.BooleanMobiusCarry.BooleanMobiusCarryCertificate.reconstructsSupport",
              "PalomarCorpus.E257.BooleanMobiusCarry.exists_booleanMobiusCarry_of_support_fraction",
              "PalomarCorpus.E257.BooleanMobiusCarry.exists_normalized_support_fraction_iff_exists_booleanMobiusCarry",
              "PalomarCorpus.E257.BooleanMobiusCarry.support_fraction_of_booleanMobiusCarry",
              "PalomarCorpus.E257.DivisibilityWeightedSupport.divisibilityWeightedClaim",
              "PalomarCorpus.E257.DyadicObservationSummability.dyadic_supportObservationMass_sum_le",
              "PalomarCorpus.E257.DyadicObservationSummability.summable_dyadic_supportObservationMass",
              "PalomarCorpus.E257.DyadicObservationSummability.tendsto_dyadic_supportObservationMass_mean",
              "PalomarCorpus.E257.FairCoding.fairCoding_pushforward_eq_volume_restrict",
              "PalomarCorpus.E257.FairCoding.fairCoding_rational_values_null",
              "PalomarCorpus.E257.FairCoding.measurePreserving_fairCoding",
              "PalomarCorpus.E257.FinitePeriodNoncollapse.finite_period_noncollapse_rat_den",
              "PalomarCorpus.E257.FinitePeriodNoncollapse.lcm_lt_den_finiteErdosSum",
              "PalomarCorpus.E257.FourNinthsRepairWindows.exists_repair_in_sqrt_window",
              "PalomarCorpus.E257.FourNinthsRepairWindows.four_ninths_mem_iff_repairCofinal",
              "PalomarCorpus.E257.FourNinthsRepairWindows.four_ninths_mem_iff_repair_sqrt_windows",
              "PalomarCorpus.E257.FourNinthsRepairWindows.four_ninths_not_mem_of_strict_sqrt_window",
              "PalomarCorpus.E257.GeneralRepairCriterion.mem_iff_greedyBinaryDefect_cofinal_repairs",
              "PalomarCorpus.E257.GeneralRepairCriterion.mem_iff_greedyBinaryDefect_sqrt_windows",
              "PalomarCorpus.E257.LiteralWeightedCover.exists_weighted_not_strengthened_host",
              "PalomarCorpus.E257.LiteralWeightedCover.exists_weighted_obstruction_with_mixed_heredity",
              "PalomarCorpus.E257.MixedWeightedCover.mixedSupportClaim",
              "PalomarCorpus.E257.PositiveSkipEquivalence.cofinalPositiveHalfGreedySkips_iff_half_mem",
              "PalomarCorpus.E257.PositiveSkipEquivalence.greedyMersenneRemainderRat_half_pos",
              "PalomarCorpus.E257.RationalMembership.greedyMersenneSkippedSupport_infinite_iff_cofinal_skips",
              "PalomarCorpus.E257.RationalMembership.infinite_greedyMersenneSkippedSupport_of_rat_mem",
              "PalomarCorpus.E257.RationalMembership.rat_mem_mersenneAchievementSet_iff_cofinal_greedy_skips",
              "PalomarCorpus.E257.RationalMembership.rat_mem_mersenneAchievementSet_iff_greedySkippedSupport_infinite",
              "PalomarCorpus.E257.RationalTailRigidity.dyadic_support_fraction_reciprocalMass_diverges_or_gt_one",
              "PalomarCorpus.E257.RationalTailRigidity.exists_unbounded_shifted_odd_tail_nat_state_of_support_fraction",
              "PalomarCorpus.E257.RationalTailRigidity.one_div_oddOrder_le_reciprocalMass_of_support_fraction",
              "PalomarCorpus.E257.RationalTailRigidity.supportCoeffZeroWindow_length_le_eps_logb_add",
              "PalomarCorpus.E257.ReciprocalSupport.irrational_supportPowerSeries_of_summable_reciprocal",
              "PalomarCorpus.E257.ScaledGreedyTrap.mem_mersenneAchievementSet_iff_scaledRemainder_cofinallyBounded",
              "PalomarCorpus.E257.ScaledGreedyTrap.mersenneAchievementSet_eq_scaledGreedyTrap",
              "PalomarCorpus.E257.ScaledGreedyTrap.one_div_twentyOne_mem_iff_scaledLowerBranchCofinally",
              "PalomarCorpus.E257.ScaledGreedyTrap.one_div_twentyOne_mem_iff_scaledRemainder_cofinallyBounded",
              "PalomarCorpus.E257.ScaledGreedyTrap.rat_mem_mersenneAchievementSet_iff_scaledLowerBranchCofinally",
              "PalomarCorpus.E257.ScaledGreedyTrap.scaledGreedyRemainder_tendsto_atTop_of_not_mem",
              "PalomarCorpus.E257.TerminalScaledVanishing.terminalScaledVanishing_completeCounterexample",
              "PalomarCorpus.E257.TwentyOneFatalBranch.one_div_twenty_one_mem_iff_not_fatalAlignedBranch",
              "PalomarCorpus.E257.TwentyOneFatalBranch.one_div_twenty_one_mem_mersenneAchievementSet_of_closedLowerStates",
              "PalomarCorpus.E257.TwentyOneFatalBranch.twentyOneClosedRow_forces_quotientGreedy",
              "PalomarCorpus.E257.TwentyOneFatalBranch.twentyOneFatalAlignedBranch_eventually_affine_supercapacity",
              "PalomarCorpus.E257.TwentyOneFatalBranch.twentyOneFatalAlignedBranch_eventually_strict_supercapacity",
              "PalomarCorpus.E257.VariableExponentCover.strengthenedPositiveCoverClaim"
            ],
            "status": "registration_requested",
            "observed_at": "2026-10-09T15:50:27.855436+00:00",
            "registered_url": null,
            "verification_run_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/35186739364",
            "observation_basis": "maintainer_authenticated_status",
            "publication_blocker": {
              "reason": "unsupported_lean_version",
              "summary": "The publication renderer rejected the reviewed Lean 4.30.0 source because its current minimum is Lean 4.35.0-rc2. Palomar must repair rendering and retry this registration; sending consent again does not resume it.",
              "evidence_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/37953891799",
              "observed_at": "2026-10-09T15:50:27.855436+00:00"
            }
          },
          {
            "entry": "ExternalVerification257ReciprocalSupport",
            "title": "Erdős #257 — reciprocal support",
            "problem_ids": [
              "erdos_257"
            ],
            "repository": "wcook04/plectis-erdos-lean",
            "commit": "c39cea6a976747d132a848d26f110b9c608d5a45",
            "comparator_config_path": "ExternalVerification257ReciprocalSupport/comparator.json",
            "formalization_metadata_path": "ExternalVerification257ReciprocalSupport/formalization.yaml",
            "theorem_names": [
              "Erdos249257.ExternalVerification257ReciprocalSupport.irrational_supportPowerSeries_of_summable_reciprocal"
            ],
            "status": "registration_requested",
            "observed_at": "2026-10-09T15:33:04Z",
            "registered_url": null,
            "verification_run_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/35192583926",
            "observation_basis": "maintainer_authenticated_status",
            "publication_blocker": {
              "reason": "unsupported_lean_version",
              "summary": "The publication renderer rejected the reviewed Lean 4.29.0 source because its current minimum is Lean 4.35.0-rc2. Palomar must repair rendering and retry this registration; sending consent again does not resume it.",
              "evidence_url": "https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/37949424576",
              "observed_at": "2026-10-09T15:33:04Z"
            }
          }
        ],
        "boundary": "Dated observations of separately identified historical submission editions. One edition is registered. Three existing reviews have registration consent, and all three have failed publication renders under the newer Lean minimum. These are not three published records. Overlapping selections do not count as new mathematics, and no outcome transfers to another commit, repository or declaration by name alone. This inventory covers the registered edition and the three requests of 9 October, not every historical submission.",
        "counts": {
          "registered": 1,
          "registration_requested": 3,
          "publication_blocked": 3
        },
        "source": "../palomar-registry-status.json",
        "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/verification/palomar_registry_status.json"
      }
    },
    {
      "id": "lean-module:Erdos249257.ActualForeignResidueProjection",
      "kind": "lean_module",
      "label": "Erdos249257.ActualForeignResidueProjection",
      "path": "lean/Erdos249257/ActualForeignResidueProjection.lean",
      "role": "Finite foreign-residue projection consumer",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ActualForeignResidueProjection.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ActualForeignResidueProjection.lean"
    },
    {
      "id": "lean-module:Erdos249257.AdelicHeightObstruction",
      "kind": "lean_module",
      "label": "Erdos249257.AdelicHeightObstruction",
      "path": "lean/Erdos249257/AdelicHeightObstruction.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AdelicHeightObstruction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AdelicHeightObstruction.lean"
    },
    {
      "id": "lean-module:Erdos249257.AdjacentCarryTube",
      "kind": "lean_module",
      "label": "Erdos249257.AdjacentCarryTube",
      "path": "lean/Erdos249257/AdjacentCarryTube.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AdjacentCarryTube.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AdjacentCarryTube.lean"
    },
    {
      "id": "lean-module:Erdos249257.AdjacentPhaseSeparation",
      "kind": "lean_module",
      "label": "Erdos249257.AdjacentPhaseSeparation",
      "path": "lean/Erdos249257/AdjacentPhaseSeparation.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AdjacentPhaseSeparation.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AdjacentPhaseSeparation.lean"
    },
    {
      "id": "lean-module:Erdos249257.AllBaseReciprocalSupportIrrationality",
      "kind": "lean_module",
      "label": "Erdos249257.AllBaseReciprocalSupportIrrationality",
      "path": "lean/Erdos249257/AllBaseReciprocalSupportIrrationality.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AllBaseReciprocalSupportIrrationality.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AllBaseReciprocalSupportIrrationality.lean"
    },
    {
      "id": "lean-module:Erdos249257.AllBaseTotientKernel",
      "kind": "lean_module",
      "label": "Erdos249257.AllBaseTotientKernel",
      "path": "lean/Erdos249257/AllBaseTotientKernel.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AllBaseTotientKernel.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/AllBaseTotientKernel.lean"
    },
    {
      "id": "lean-module:Erdos249257.BinaryTailWindowTransfer",
      "kind": "lean_module",
      "label": "Erdos249257.BinaryTailWindowTransfer",
      "path": "lean/Erdos249257/BinaryTailWindowTransfer.lean",
      "role": "Binary tail-window transfer interfaces",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BinaryTailWindowTransfer.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BinaryTailWindowTransfer.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusCarry",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusCarry",
      "path": "lean/Erdos249257/BooleanMobiusCarry.lean",
      "role": "Boolean-Mobius carry coordinates",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCarry.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCarry.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusCofinalExactRows",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusCofinalExactRows",
      "path": "lean/Erdos249257/BooleanMobiusCofinalExactRows.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCofinalExactRows.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCofinalExactRows.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusCriticalCapacityCofinal",
      "path": "lean/Erdos249257/BooleanMobiusCriticalCapacityCofinal.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCriticalCapacityCofinal.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCriticalCapacityCofinal.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityGeometric",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusCriticalCapacityGeometric",
      "path": "lean/Erdos249257/BooleanMobiusCriticalCapacityGeometric.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCriticalCapacityGeometric.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusCriticalCapacityGeometric.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusExactRowCrossing",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusExactRowCrossing",
      "path": "lean/Erdos249257/BooleanMobiusExactRowCrossing.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowCrossing.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowCrossing.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusExactRowDichotomy",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusExactRowDichotomy",
      "path": "lean/Erdos249257/BooleanMobiusExactRowDichotomy.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowDichotomy.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowDichotomy.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusExactRowDoubling",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusExactRowDoubling",
      "path": "lean/Erdos249257/BooleanMobiusExactRowDoubling.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowDoubling.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowDoubling.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusExactRowRankTwo",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusExactRowRankTwo",
      "path": "lean/Erdos249257/BooleanMobiusExactRowRankTwo.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowRankTwo.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowRankTwo.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusExactRowSeed",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusExactRowSeed",
      "path": "lean/Erdos249257/BooleanMobiusExactRowSeed.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowSeed.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactRowSeed.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusExactTransition",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusExactTransition",
      "path": "lean/Erdos249257/BooleanMobiusExactTransition.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactTransition.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusExactTransition.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusGlobalRepair",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusGlobalRepair",
      "path": "lean/Erdos249257/BooleanMobiusGlobalRepair.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusGlobalRepair.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusGlobalRepair.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusGreedyReduction",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusGreedyReduction",
      "path": "lean/Erdos249257/BooleanMobiusGreedyReduction.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusGreedyReduction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusGreedyReduction.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusLocalRepair",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusLocalRepair",
      "path": "lean/Erdos249257/BooleanMobiusLocalRepair.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusLocalRepair.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusLocalRepair.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusSkipRow",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusSkipRow",
      "path": "lean/Erdos249257/BooleanMobiusSkipRow.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkipRow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkipRow.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusSkipRowCofinal",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusSkipRowCofinal",
      "path": "lean/Erdos249257/BooleanMobiusSkipRowCofinal.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkipRowCofinal.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkipRowCofinal.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusSkippedCoreCriticalCapacity",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusSkippedCoreCriticalCapacity",
      "path": "lean/Erdos249257/BooleanMobiusSkippedCoreCriticalCapacity.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkippedCoreCriticalCapacity.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkippedCoreCriticalCapacity.lean"
    },
    {
      "id": "lean-module:Erdos249257.BooleanMobiusSkippedCoreExactRow",
      "kind": "lean_module",
      "label": "Erdos249257.BooleanMobiusSkippedCoreExactRow",
      "path": "lean/Erdos249257/BooleanMobiusSkippedCoreExactRow.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkippedCoreExactRow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/BooleanMobiusSkippedCoreExactRow.lean"
    },
    {
      "id": "lean-module:Erdos249257.CampbellShiftSynchronization",
      "kind": "lean_module",
      "label": "Erdos249257.CampbellShiftSynchronization",
      "path": "lean/Erdos249257/CampbellShiftSynchronization.lean",
      "role": "Campbell shift synchronization for the half target",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CampbellShiftSynchronization.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CampbellShiftSynchronization.lean"
    },
    {
      "id": "lean-module:Erdos249257.CarrySurvivorExtinction",
      "kind": "lean_module",
      "label": "Erdos249257.CarrySurvivorExtinction",
      "path": "lean/Erdos249257/CarrySurvivorExtinction.lean",
      "role": "Multiple-period collapse",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CarrySurvivorExtinction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CarrySurvivorExtinction.lean"
    },
    {
      "id": "lean-module:Erdos249257.CertificateKernel",
      "kind": "lean_module",
      "label": "Erdos249257.CertificateKernel",
      "path": "lean/Erdos249257/CertificateKernel.lean",
      "role": "Assembled theorem kernel and headline interfaces",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CertificateKernel.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CertificateKernel.lean"
    },
    {
      "id": "lean-module:Erdos249257.CofinalStripReturn",
      "kind": "lean_module",
      "label": "Erdos249257.CofinalStripReturn",
      "path": "lean/Erdos249257/CofinalStripReturn.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CofinalStripReturn.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CofinalStripReturn.lean"
    },
    {
      "id": "lean-module:Erdos249257.CompositeDilationDefect",
      "kind": "lean_module",
      "label": "Erdos249257.CompositeDilationDefect",
      "path": "lean/Erdos249257/CompositeDilationDefect.lean",
      "role": "Composite support-dilation defect identity",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CompositeDilationDefect.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CompositeDilationDefect.lean"
    },
    {
      "id": "lean-module:Erdos249257.CurvatureCarry",
      "kind": "lean_module",
      "label": "Erdos249257.CurvatureCarry",
      "path": "lean/Erdos249257/CurvatureCarry.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CurvatureCarry.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CurvatureCarry.lean"
    },
    {
      "id": "lean-module:Erdos249257.CyclicTensorMobiusShadow",
      "kind": "lean_module",
      "label": "Erdos249257.CyclicTensorMobiusShadow",
      "path": "lean/Erdos249257/CyclicTensorMobiusShadow.lean",
      "role": "Cyclic tensor identities for the Mobius shadow",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CyclicTensorMobiusShadow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CyclicTensorMobiusShadow.lean"
    },
    {
      "id": "lean-module:Erdos249257.CyclotomicProjectionOfShadow",
      "kind": "lean_module",
      "label": "Erdos249257.CyclotomicProjectionOfShadow",
      "path": "lean/Erdos249257/CyclotomicProjectionOfShadow.lean",
      "role": "Cyclotomic projections of the Mobius shadow",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CyclotomicProjectionOfShadow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/CyclotomicProjectionOfShadow.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalFlexibleOddWindowAffine",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalFlexibleOddWindowAffine",
      "path": "lean/Erdos249257/DiagonalFlexibleOddWindowAffine.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalFlexibleOddWindowAffine.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalFlexibleOddWindowAffine.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalFlexibleOddWindowSupply",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalFlexibleOddWindowSupply",
      "path": "lean/Erdos249257/DiagonalFlexibleOddWindowSupply.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalFlexibleOddWindowSupply.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalFlexibleOddWindowSupply.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalFreshLossBridge",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalFreshLossBridge",
      "path": "lean/Erdos249257/DiagonalFreshLossBridge.lean",
      "role": "Fresh-loss projection and suffix-supply reduction",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalFreshLossBridge.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalFreshLossBridge.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificateT64Endpoint",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificateT64Endpoint",
      "path": "lean/Erdos249257/DiagonalPincerCertificateT64Endpoint.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificateT64Endpoint.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificateT64Endpoint.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificates",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificates",
      "path": "lean/Erdos249257/DiagonalPincerCertificates.lean",
      "role": "Finite diagonal-pincer certificate base",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificates.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificates.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT19",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT19",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT19.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT19.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT19.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT23",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT23",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT23.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT23.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT23.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT25",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT25",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT25.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT25.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT25.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT27",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT27",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT27.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT27.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT27.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT29",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT29",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT29.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT29.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT29.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT31",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT31",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT31.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT31.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT31.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT32",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT32",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT32.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT32.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT32.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT37",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT37",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT37.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT37.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT37.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT41",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT41",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT41.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT41.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT41.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT43",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT43",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT43.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT43.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT43.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT47",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT47",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT47.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT47.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT47.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT49",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT49",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT49.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT49.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT49.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT53",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT53",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT53.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT53.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT53.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT59",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT59",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT59.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT59.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT59.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT61",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT61",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT61.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT61.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT61.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerCertificatesT64",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerCertificatesT64",
      "path": "lean/Erdos249257/DiagonalPincerCertificatesT64.lean",
      "role": "Finite diagonal-pincer certificate extension",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT64.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerCertificatesT64.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerDecomposition",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerDecomposition",
      "path": "lean/Erdos249257/DiagonalPincerDecomposition.lean",
      "role": "Exact diagonal-pincer target decomposition",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerDecomposition.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerDecomposition.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level0A",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level0A",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level0A.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level0A.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level0A.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level0B",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level0B",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level0B.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level0B.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level0B.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level1A",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level1A",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level1A.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level1A.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level1A.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level1B",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level1B",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level1B.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level1B.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level1B.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level2A",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level2A",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level2A.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level2A.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level2A.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.ClosureT64.Level2B",
      "kind": "lean_module",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level2B.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level2B.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/ClosureT64/Level2B.lean"
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      "role": "Finite diagonal prime-certificate shard",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime225370565575711.lean",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime22590511471547.lean",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime2297338423.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime2297338423.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime2297338423.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime2302624777.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime2302624777.lean",
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime255550753.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime262790815093.lean",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime262886497.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime262886497.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime2641630853.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime264586369.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime26581748542603.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime26581748542603.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime266851416720089.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime266851416720089.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime266851416720089.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime26771144401.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime26771144401.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime26771144401.lean"
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime3651003162326521.lean",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime3651003162326521.lean"
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      "role": "Finite diagonal prime-certificate shard",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime3667077183983.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime36750397.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime36750397.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime368512303.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime368512303.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime36975198103.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime36975198103.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime36975198103.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime3702655202401.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime3702655202401.lean",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime40185923.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime40185923.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime40185923.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime402753765797.lean",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime40430111.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime40430111.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime40965791.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime40965791.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4130492505504241.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4130492505504241.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4130492505504241.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime41511618511829.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime41511618511829.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime41511618511829.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime41583179525359.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime41583179525359.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime41583179525359.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime421119071.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime421119071.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime421119071.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime422621401.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime422621401.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime422621401.lean"
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    {
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      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime42406327",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime42406327.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime42406327.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime42406327.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.Prime426598383733",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime426598383733",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime426598383733.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime426598383733.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime426598383733.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.Prime43215661814873",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime43215661814873",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43215661814873.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43215661814873.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43215661814873.lean"
    },
    {
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime43693841",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43693841.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43693841.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43693841.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.Prime43707991",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime43707991",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43707991.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43707991.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43707991.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.Prime438120379479182443",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime438120379479182443",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime438120379479182443.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime438120379479182443.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime438120379479182443.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.Prime43913777",
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime43913777",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43913777.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43913777.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime43913777.lean"
    },
    {
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime440869801.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime440869801.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime440869801.lean"
    },
    {
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime444482741",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime444482741.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime444482741.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime444482741.lean"
    },
    {
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime44544251",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime44544251.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime44544251.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime44544251.lean"
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    {
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime4461857401",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4461857401.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4461857401.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4461857401.lean"
    },
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime44709187",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime44709187.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime44709187.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime44709187.lean"
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    {
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      "kind": "lean_module",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime448521808841.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime448521808841.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime448521808841.lean"
    },
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime448551817085829601",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime448551817085829601.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime448551817085829601.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime448551817085829601.lean"
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime45293161",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime45293161.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime45293161.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime45293161.lean"
    },
    {
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      "kind": "lean_module",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4537773511.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4537773511.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4537773511.lean"
    },
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime45726156110691367",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime45726156110691367.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime45726156110691367.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime45726156110691367.lean"
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4579662077.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4579662077.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4579662077.lean"
    },
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime46078157",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46078157.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46078157.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46078157.lean"
    },
    {
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46558513.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46558513.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46558513.lean"
    },
    {
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime465585143.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime465585143.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime465585143.lean"
    },
    {
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime465585151.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime465585151.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime465585151.lean"
    },
    {
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46558517.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46558517.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46558517.lean"
    },
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime46640743",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46640743.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46640743.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime46640743.lean"
    },
    {
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime472210373.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime472210373.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime472210373.lean"
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    {
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      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime4758099209",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4758099209.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4758099209.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4758099209.lean"
    },
    {
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime478361953",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime478361953.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime478361953.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime478361953.lean"
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      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime4813451763121",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4813451763121.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4813451763121.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4813451763121.lean"
    },
    {
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      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime48276289",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime48276289.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime48276289.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime48276289.lean"
    },
    {
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      "kind": "lean_module",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime48327828947.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime48327828947.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime48327828947.lean"
    },
    {
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      "kind": "lean_module",
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      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4857175351079.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4857175351079.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4857175351079.lean"
    },
    {
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      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime4868004216435361",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4868004216435361.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4868004216435361.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime4868004216435361.lean"
    },
    {
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      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime491213659",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime491213659.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime491213659.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime491213659.lean"
    },
    {
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      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime49571861",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime49571861.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime49571861.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime49571861.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.Prime495761933",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime495761933",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime495761933.lean",
      "role": "Finite diagonal prime-certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime495761933.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime495761933.lean"
    },
    {
      "id": "lean-module:Erdos249257.DiagonalPincerPrimeCertificates.Prime496735124126057",
      "kind": "lean_module",
      "label": "Erdos249257.DiagonalPincerPrimeCertificates.Prime496735124126057",
      "path": "lean/Erdos249257/DiagonalPincerPrimeCertificates/Prime496735124126057.lean",
      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Finite diagonal prime-certificate shard",
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      "role": "Generated finite certificate shard",
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      "role": "Generated finite certificate shard",
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      "label": "Erdos249257.GeneratedCertificates.b2_L210_A21371",
      "path": "lean/Erdos249257/GeneratedCertificates/b2_L210_A21371.lean",
      "role": "Generated finite certificate shard",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GeneratedCertificates/b2_L210_A21371.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GeneratedCertificates/b2_L210_A21371.lean"
    },
    {
      "id": "lean-module:Erdos249257.GenericTailOrbitRigidity",
      "kind": "lean_module",
      "label": "Erdos249257.GenericTailOrbitRigidity",
      "path": "lean/Erdos249257/GenericTailOrbitRigidity.lean",
      "role": "Tempered tail-orbit rationality criterion",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GenericTailOrbitRigidity.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GenericTailOrbitRigidity.lean"
    },
    {
      "id": "lean-module:Erdos249257.GeometricCoprimality",
      "kind": "lean_module",
      "label": "Erdos249257.GeometricCoprimality",
      "path": "lean/Erdos249257/GeometricCoprimality.lean",
      "role": "Coprime-pair interpretation of the totient series",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GeometricCoprimality.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GeometricCoprimality.lean"
    },
    {
      "id": "lean-module:Erdos249257.GreedyAchievementSet",
      "kind": "lean_module",
      "label": "Erdos249257.GreedyAchievementSet",
      "path": "lean/Erdos249257/GreedyAchievementSet.lean",
      "role": "Greedy geometry and finite death certificates",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GreedyAchievementSet.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GreedyAchievementSet.lean"
    },
    {
      "id": "lean-module:Erdos249257.GreedyTrapDynamics",
      "kind": "lean_module",
      "label": "Erdos249257.GreedyTrapDynamics",
      "path": "lean/Erdos249257/GreedyTrapDynamics.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GreedyTrapDynamics.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/GreedyTrapDynamics.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCarryCeilParentContraction",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCarryCeilParentContraction",
      "path": "lean/Erdos249257/HalfCarryCeilParentContraction.lean",
      "role": "Fixed-coefficient rewind contraction",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryCeilParentContraction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryCeilParentContraction.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCarryCofinalWindowOrSeamConsumer",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCarryCofinalWindowOrSeamConsumer",
      "path": "lean/Erdos249257/HalfCarryCofinalWindowOrSeamConsumer.lean",
      "role": "Mixed cofinal half-carry fan-in",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryCofinalWindowOrSeamConsumer.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryCofinalWindowOrSeamConsumer.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCarryProtectedSeamConsumer",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCarryProtectedSeamConsumer",
      "path": "lean/Erdos249257/HalfCarryProtectedSeamConsumer.lean",
      "role": "Localized protected one-hole seam consumer",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryProtectedSeamConsumer.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryProtectedSeamConsumer.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCarryReachability",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCarryReachability",
      "path": "lean/Erdos249257/HalfCarryReachability.lean",
      "role": "Half-carry reachability and compactness",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryReachability.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryReachability.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCarryRewindPhase",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCarryRewindPhase",
      "path": "lean/Erdos249257/HalfCarryRewindPhase.lean",
      "role": "Realized fixed-coefficient rewind phase",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryRewindPhase.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarryRewindPhase.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCarrySelectedWindow",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCarrySelectedWindow",
      "path": "lean/Erdos249257/HalfCarrySelectedWindow.lean",
      "role": "Selected protected half-carry windows",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarrySelectedWindow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarrySelectedWindow.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCarrySelectedWindowBase",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCarrySelectedWindowBase",
      "path": "lean/Erdos249257/HalfCarrySelectedWindowBase.lean",
      "role": "Computed depth-18 selected half-carry window base",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarrySelectedWindowBase.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCarrySelectedWindowBase.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCutLocator",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCutLocator",
      "path": "lean/Erdos249257/HalfCutLocator.lean",
      "role": "Fatal-gap locator for the half target",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCutLocator.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCutLocator.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderBoundaryPulse",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderBoundaryPulse",
      "path": "lean/Erdos249257/HalfCylinderBoundaryPulse.lean",
      "role": "Boundary-pulse normalization at the largest-skip crossing",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderBoundaryPulse.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderBoundaryPulse.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderConcreteSeamAdapter",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderConcreteSeamAdapter",
      "path": "lean/Erdos249257/HalfCylinderConcreteSeamAdapter.lean",
      "role": "Concrete finite seam adapter",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderConcreteSeamAdapter.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderConcreteSeamAdapter.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFalseBitSupply",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFalseBitSupply",
      "path": "lean/Erdos249257/HalfCylinderFalseBitSupply.lean",
      "role": "False-bit supply for the half seam",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFalseBitSupply.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFalseBitSupply.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFatalGapRightTail",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFatalGapRightTail",
      "path": "lean/Erdos249257/HalfCylinderFatalGapRightTail.lean",
      "role": "Fatal-gap and eventual-right seam classification for the half target",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFatalGapRightTail.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFatalGapRightTail.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFinalMiddleCellEscape",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFinalMiddleCellEscape",
      "path": "lean/Erdos249257/HalfCylinderFinalMiddleCellEscape.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFinalMiddleCellEscape.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFinalMiddleCellEscape.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFinalMiddleTailSocket",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFinalMiddleTailSocket",
      "path": "lean/Erdos249257/HalfCylinderFinalMiddleTailSocket.lean",
      "role": "Analytic tail socket for the final middle seam cells",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFinalMiddleTailSocket.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFinalMiddleTailSocket.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFiniteShadow",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFiniteShadow",
      "path": "lean/Erdos249257/HalfCylinderFiniteShadow.lean",
      "role": "Finite shadows of the half cylinder",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFiniteShadow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFiniteShadow.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFixedTailSocket",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFixedTailSocket",
      "path": "lean/Erdos249257/HalfCylinderFixedTailSocket.lean",
      "role": "Fixed-tail survival classification for half-cylinder skips",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFixedTailSocket.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFixedTailSocket.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFloorErrorReset",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFloorErrorReset",
      "path": "lean/Erdos249257/HalfCylinderFloorErrorReset.lean",
      "role": "Floor-error reset for the half seam",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFloorErrorReset.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFloorErrorReset.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderFullShellSeamBridge",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderFullShellSeamBridge",
      "path": "lean/Erdos249257/HalfCylinderFullShellSeamBridge.lean",
      "role": "Full-shell seam bridge for the half target",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFullShellSeamBridge.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderFullShellSeamBridge.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderHalfMembershipClassification",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderHalfMembershipClassification",
      "path": "lean/Erdos249257/HalfCylinderHalfMembershipClassification.lean",
      "role": "Positive half-membership classification in seam coordinates",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderHalfMembershipClassification.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderHalfMembershipClassification.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderIntegerGreedy",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderIntegerGreedy",
      "path": "lean/Erdos249257/HalfCylinderIntegerGreedy.lean",
      "role": "Integer-greedy first-wrap seam reduction",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderIntegerGreedy.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderIntegerGreedy.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderLargestSkipGap",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderLargestSkipGap",
      "path": "lean/Erdos249257/HalfCylinderLargestSkipGap.lean",
      "role": "Largest skipped-rank gap and successor propagation for the half seam",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderLargestSkipGap.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderLargestSkipGap.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderLargestSkipInduction",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderLargestSkipInduction",
      "path": "lean/Erdos249257/HalfCylinderLargestSkipInduction.lean",
      "role": "Largest-skip induction from a first-crossing producer socket",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderLargestSkipInduction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderLargestSkipInduction.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderLastProducerContradiction",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderLastProducerContradiction",
      "path": "lean/Erdos249257/HalfCylinderLastProducerContradiction.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderLastProducerContradiction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderLastProducerContradiction.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderMiddleCarryLowerBound",
      "path": "lean/Erdos249257/HalfCylinderMiddleCarryLowerBound.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderMiddleCarryLowerBound.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderMiddleCarryLowerBound.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderProducerCarrySocket",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderProducerCarrySocket",
      "path": "lean/Erdos249257/HalfCylinderProducerCarrySocket.lean",
      "role": "Producer-carry and future-tail comparison socket",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderProducerCarrySocket.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderProducerCarrySocket.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderProducerLowerBound",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderProducerLowerBound",
      "path": "lean/Erdos249257/HalfCylinderProducerLowerBound.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderProducerLowerBound.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderProducerLowerBound.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderQuarterBandEndpoints",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderQuarterBandEndpoints",
      "path": "lean/Erdos249257/HalfCylinderQuarterBandEndpoints.lean",
      "role": "Quarter-band endpoint cells for adjacent half-cylinder cuts",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderQuarterBandEndpoints.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderQuarterBandEndpoints.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderResetDeficitEscape",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderResetDeficitEscape",
      "path": "lean/Erdos249257/HalfCylinderResetDeficitEscape.lean",
      "role": "Reset-deficit escape geometry for the largest-skip crossing",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderResetDeficitEscape.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderResetDeficitEscape.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderSeamLimit",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderSeamLimit",
      "path": "lean/Erdos249257/HalfCylinderSeamLimit.lean",
      "role": "Seam-limit reduction for the half target",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSeamLimit.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSeamLimit.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderSeamProducerAlignment",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderSeamProducerAlignment",
      "path": "lean/Erdos249257/HalfCylinderSeamProducerAlignment.lean",
      "role": "Seam-to-producer carry alignment identity",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSeamProducerAlignment.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSeamProducerAlignment.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderSkippedEndpointClassifier",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderSkippedEndpointClassifier",
      "path": "lean/Erdos249257/HalfCylinderSkippedEndpointClassifier.lean",
      "role": "Skipped-endpoint classifier for the half seam",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSkippedEndpointClassifier.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSkippedEndpointClassifier.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderSkippedRankLimit",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderSkippedRankLimit",
      "path": "lean/Erdos249257/HalfCylinderSkippedRankLimit.lean",
      "role": "Skipped-rank limit for the half seam",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSkippedRankLimit.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderSkippedRankLimit.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfCylinderUpperResetBandCertificates",
      "kind": "lean_module",
      "label": "Erdos249257.HalfCylinderUpperResetBandCertificates",
      "path": "lean/Erdos249257/HalfCylinderUpperResetBandCertificates.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderUpperResetBandCertificates.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfCylinderUpperResetBandCertificates.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfDivisorUnitDrop",
      "kind": "lean_module",
      "label": "Erdos249257.HalfDivisorUnitDrop",
      "path": "lean/Erdos249257/HalfDivisorUnitDrop.lean",
      "role": "Half-divisor unit coefficient drop at the feedback row",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfDivisorUnitDrop.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfDivisorUnitDrop.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfFinalMiddlePhaseSieve",
      "kind": "lean_module",
      "label": "Erdos249257.HalfFinalMiddlePhaseSieve",
      "path": "lean/Erdos249257/HalfFinalMiddlePhaseSieve.lean",
      "role": "Rank-26 final-middle phase sieve for the half seam",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfFinalMiddlePhaseSieve.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfFinalMiddlePhaseSieve.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfGapMass",
      "kind": "lean_module",
      "label": "Erdos249257.HalfGapMass",
      "path": "lean/Erdos249257/HalfGapMass.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGapMass.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGapMass.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfGreedyFatalGap",
      "kind": "lean_module",
      "label": "Erdos249257.HalfGreedyFatalGap",
      "path": "lean/Erdos249257/HalfGreedyFatalGap.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGreedyFatalGap.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGreedyFatalGap.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfGreedyTwoThirdsBand",
      "kind": "lean_module",
      "label": "Erdos249257.HalfGreedyTwoThirdsBand",
      "path": "lean/Erdos249257/HalfGreedyTwoThirdsBand.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGreedyTwoThirdsBand.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGreedyTwoThirdsBand.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfGreedyUnitPrefix",
      "kind": "lean_module",
      "label": "Erdos249257.HalfGreedyUnitPrefix",
      "path": "lean/Erdos249257/HalfGreedyUnitPrefix.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGreedyUnitPrefix.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfGreedyUnitPrefix.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfTrappingReturnCarry",
      "kind": "lean_module",
      "label": "Erdos249257.HalfTrappingReturnCarry",
      "path": "lean/Erdos249257/HalfTrappingReturnCarry.lean",
      "role": "Half-trapping reverse-carry interface",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfTrappingReturnCarry.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfTrappingReturnCarry.lean"
    },
    {
      "id": "lean-module:Erdos249257.HalfUpperResetCriticalBand",
      "kind": "lean_module",
      "label": "Erdos249257.HalfUpperResetCriticalBand",
      "path": "lean/Erdos249257/HalfUpperResetCriticalBand.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfUpperResetCriticalBand.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/HalfUpperResetCriticalBand.lean"
    },
    {
      "id": "lean-module:Erdos249257.IncidenceQuotientHermitePade",
      "kind": "lean_module",
      "label": "Erdos249257.IncidenceQuotientHermitePade",
      "path": "lean/Erdos249257/IncidenceQuotientHermitePade.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/IncidenceQuotientHermitePade.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/IncidenceQuotientHermitePade.lean"
    },
    {
      "id": "lean-module:Erdos249257.JointExponentTransport",
      "kind": "lean_module",
      "label": "Erdos249257.JointExponentTransport",
      "path": "lean/Erdos249257/JointExponentTransport.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/JointExponentTransport.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/JointExponentTransport.lean"
    },
    {
      "id": "lean-module:Erdos249257.LambertDiagonalEnclosure",
      "kind": "lean_module",
      "label": "Erdos249257.LambertDiagonalEnclosure",
      "path": "lean/Erdos249257/LambertDiagonalEnclosure.lean",
      "role": "Lambert diagonal enclosure reduction",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LambertDiagonalEnclosure.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LambertDiagonalEnclosure.lean"
    },
    {
      "id": "lean-module:Erdos249257.LambertProjectedNumeratorGap",
      "kind": "lean_module",
      "label": "Erdos249257.LambertProjectedNumeratorGap",
      "path": "lean/Erdos249257/LambertProjectedNumeratorGap.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LambertProjectedNumeratorGap.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LambertProjectedNumeratorGap.lean"
    },
    {
      "id": "lean-module:Erdos249257.LcmConeFlatness",
      "kind": "lean_module",
      "label": "Erdos249257.LcmConeFlatness",
      "path": "lean/Erdos249257/LcmConeFlatness.lean",
      "role": "Cone-flatness and certificate completeness",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmConeFlatness.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmConeFlatness.lean"
    },
    {
      "id": "lean-module:Erdos249257.LcmConeNonflat",
      "kind": "lean_module",
      "label": "Erdos249257.LcmConeNonflat",
      "path": "lean/Erdos249257/LcmConeNonflat.lean",
      "role": "Joint cone non-flatness refuter",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmConeNonflat.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmConeNonflat.lean"
    },
    {
      "id": "lean-module:Erdos249257.LcmDiagonalReduction",
      "kind": "lean_module",
      "label": "Erdos249257.LcmDiagonalReduction",
      "path": "lean/Erdos249257/LcmDiagonalReduction.lean",
      "role": "One-parameter lcm-diagonal reduction",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmDiagonalReduction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmDiagonalReduction.lean"
    },
    {
      "id": "lean-module:Erdos249257.LcmFactorIdealPulseObstruction",
      "kind": "lean_module",
      "label": "Erdos249257.LcmFactorIdealPulseObstruction",
      "path": "lean/Erdos249257/LcmFactorIdealPulseObstruction.lean",
      "role": "LCM factor-ideal anchor-pulse obstruction",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmFactorIdealPulseObstruction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/LcmFactorIdealPulseObstruction.lean"
    },
    {
      "id": "lean-module:Erdos249257.MaximalOmegaLayer",
      "kind": "lean_module",
      "label": "Erdos249257.MaximalOmegaLayer",
      "path": "lean/Erdos249257/MaximalOmegaLayer.lean",
      "role": "Mixed prime-power support-layer identities",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MaximalOmegaLayer.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MaximalOmegaLayer.lean"
    },
    {
      "id": "lean-module:Erdos249257.MersenneLambertLadder",
      "kind": "lean_module",
      "label": "Erdos249257.MersenneLambertLadder",
      "path": "lean/Erdos249257/MersenneLambertLadder.lean",
      "role": "Mersenne-Lambert identities",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneLambertLadder.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneLambertLadder.lean"
    },
    {
      "id": "lean-module:Erdos249257.MersenneShadowCyclotomicNoncollapse",
      "kind": "lean_module",
      "label": "Erdos249257.MersenneShadowCyclotomicNoncollapse",
      "path": "lean/Erdos249257/MersenneShadowCyclotomicNoncollapse.lean",
      "role": "Cyclotomic noncollapse in the Mersenne shadow",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneShadowCyclotomicNoncollapse.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneShadowCyclotomicNoncollapse.lean"
    },
    {
      "id": "lean-module:Erdos249257.MersenneShadowDenominatorGrowth",
      "kind": "lean_module",
      "label": "Erdos249257.MersenneShadowDenominatorGrowth",
      "path": "lean/Erdos249257/MersenneShadowDenominatorGrowth.lean",
      "role": "Exact denominator growth in the Mersenne shadow",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneShadowDenominatorGrowth.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneShadowDenominatorGrowth.lean"
    },
    {
      "id": "lean-module:Erdos249257.MersenneTailAtoms",
      "kind": "lean_module",
      "label": "Erdos249257.MersenneTailAtoms",
      "path": "lean/Erdos249257/MersenneTailAtoms.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneTailAtoms.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MersenneTailAtoms.lean"
    },
    {
      "id": "lean-module:Erdos249257.MobiusSignSupportNoGo",
      "kind": "lean_module",
      "label": "Erdos249257.MobiusSignSupportNoGo",
      "path": "lean/Erdos249257/MobiusSignSupportNoGo.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MobiusSignSupportNoGo.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/MobiusSignSupportNoGo.lean"
    },
    {
      "id": "lean-module:Erdos249257.PivotAntiReconstruction",
      "kind": "lean_module",
      "label": "Erdos249257.PivotAntiReconstruction",
      "path": "lean/Erdos249257/PivotAntiReconstruction.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PivotAntiReconstruction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PivotAntiReconstruction.lean"
    },
    {
      "id": "lean-module:Erdos249257.PowerTwoBitLift",
      "kind": "lean_module",
      "label": "Erdos249257.PowerTwoBitLift",
      "path": "lean/Erdos249257/PowerTwoBitLift.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PowerTwoBitLift.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PowerTwoBitLift.lean"
    },
    {
      "id": "lean-module:Erdos249257.PowerTwoCenteredBitLift",
      "kind": "lean_module",
      "label": "Erdos249257.PowerTwoCenteredBitLift",
      "path": "lean/Erdos249257/PowerTwoCenteredBitLift.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PowerTwoCenteredBitLift.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PowerTwoCenteredBitLift.lean"
    },
    {
      "id": "lean-module:Erdos249257.PrimeJumpMigration",
      "kind": "lean_module",
      "label": "Erdos249257.PrimeJumpMigration",
      "path": "lean/Erdos249257/PrimeJumpMigration.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimeJumpMigration.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimeJumpMigration.lean"
    },
    {
      "id": "lean-module:Erdos249257.PrimeJumpWindow",
      "kind": "lean_module",
      "label": "Erdos249257.PrimeJumpWindow",
      "path": "lean/Erdos249257/PrimeJumpWindow.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimeJumpWindow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimeJumpWindow.lean"
    },
    {
      "id": "lean-module:Erdos249257.PrimePowerJumpDynamics",
      "kind": "lean_module",
      "label": "Erdos249257.PrimePowerJumpDynamics",
      "path": "lean/Erdos249257/PrimePowerJumpDynamics.lean",
      "role": "Prime-power jump dynamics",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimePowerJumpDynamics.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimePowerJumpDynamics.lean"
    },
    {
      "id": "lean-module:Erdos249257.Primitive23Multiplicity",
      "kind": "lean_module",
      "label": "Erdos249257.Primitive23Multiplicity",
      "path": "lean/Erdos249257/Primitive23Multiplicity.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/Primitive23Multiplicity.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/Primitive23Multiplicity.lean"
    },
    {
      "id": "lean-module:Erdos249257.PrimitiveDeterminantLift",
      "kind": "lean_module",
      "label": "Erdos249257.PrimitiveDeterminantLift",
      "path": "lean/Erdos249257/PrimitiveDeterminantLift.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveDeterminantLift.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveDeterminantLift.lean"
    },
    {
      "id": "lean-module:Erdos249257.PrimitiveRationalGapSupply",
      "kind": "lean_module",
      "label": "Erdos249257.PrimitiveRationalGapSupply",
      "path": "lean/Erdos249257/PrimitiveRationalGapSupply.lean",
      "role": "Conditional primitive rational-gap supply interface",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveRationalGapSupply.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveRationalGapSupply.lean"
    },
    {
      "id": "lean-module:Erdos249257.PrimitiveSupportBridge",
      "kind": "lean_module",
      "label": "Erdos249257.PrimitiveSupportBridge",
      "path": "lean/Erdos249257/PrimitiveSupportBridge.lean",
      "role": "Conditional primitive-support bridge",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveSupportBridge.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveSupportBridge.lean"
    },
    {
      "id": "lean-module:Erdos249257.PrimitiveWeightCertificate",
      "kind": "lean_module",
      "label": "Erdos249257.PrimitiveWeightCertificate",
      "path": "lean/Erdos249257/PrimitiveWeightCertificate.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveWeightCertificate.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/PrimitiveWeightCertificate.lean"
    },
    {
      "id": "lean-module:Erdos249257.RadicalMobiusShadow",
      "kind": "lean_module",
      "label": "Erdos249257.RadicalMobiusShadow",
      "path": "lean/Erdos249257/RadicalMobiusShadow.lean",
      "role": "Radical structure of the Mobius shadow",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RadicalMobiusShadow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RadicalMobiusShadow.lean"
    },
    {
      "id": "lean-module:Erdos249257.RationalDenominatorSurvival",
      "kind": "lean_module",
      "label": "Erdos249257.RationalDenominatorSurvival",
      "path": "lean/Erdos249257/RationalDenominatorSurvival.lean",
      "role": "Rational denominator-survival identities",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RationalDenominatorSurvival.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RationalDenominatorSurvival.lean"
    },
    {
      "id": "lean-module:Erdos249257.RationalSupportCarrySkeleton",
      "kind": "lean_module",
      "label": "Erdos249257.RationalSupportCarrySkeleton",
      "path": "lean/Erdos249257/RationalSupportCarrySkeleton.lean",
      "role": "Residue wraps, reciprocal mass, and unbounded carries",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RationalSupportCarrySkeleton.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RationalSupportCarrySkeleton.lean"
    },
    {
      "id": "lean-module:Erdos249257.ReciprocalSupportIrrationality",
      "kind": "lean_module",
      "label": "Erdos249257.ReciprocalSupportIrrationality",
      "path": "lean/Erdos249257/ReciprocalSupportIrrationality.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ReciprocalSupportIrrationality.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ReciprocalSupportIrrationality.lean"
    },
    {
      "id": "lean-module:Erdos249257.RepunitMobiusNumerator",
      "kind": "lean_module",
      "label": "Erdos249257.RepunitMobiusNumerator",
      "path": "lean/Erdos249257/RepunitMobiusNumerator.lean",
      "role": "Repunit and Mobius-numerator identities",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RepunitMobiusNumerator.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RepunitMobiusNumerator.lean"
    },
    {
      "id": "lean-module:Erdos249257.ResidualGaugeObstruction",
      "kind": "lean_module",
      "label": "Erdos249257.ResidualGaugeObstruction",
      "path": "lean/Erdos249257/ResidualGaugeObstruction.lean",
      "role": "Residual-gauge obstruction for monomial minor criteria",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ResidualGaugeObstruction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ResidualGaugeObstruction.lean"
    },
    {
      "id": "lean-module:Erdos249257.RewindBoundaryPairCounterexample",
      "kind": "lean_module",
      "label": "Erdos249257.RewindBoundaryPairCounterexample",
      "path": "lean/Erdos249257/RewindBoundaryPairCounterexample.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RewindBoundaryPairCounterexample.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RewindBoundaryPairCounterexample.lean"
    },
    {
      "id": "lean-module:Erdos249257.RewindHalfDivisorAdapter",
      "kind": "lean_module",
      "label": "Erdos249257.RewindHalfDivisorAdapter",
      "path": "lean/Erdos249257/RewindHalfDivisorAdapter.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RewindHalfDivisorAdapter.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RewindHalfDivisorAdapter.lean"
    },
    {
      "id": "lean-module:Erdos249257.RewindSeamOperationalBridge",
      "kind": "lean_module",
      "label": "Erdos249257.RewindSeamOperationalBridge",
      "path": "lean/Erdos249257/RewindSeamOperationalBridge.lean",
      "role": "Operational bridge from rewind seams to protected next-row seams",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RewindSeamOperationalBridge.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/RewindSeamOperationalBridge.lean"
    },
    {
      "id": "lean-module:Erdos249257.SelectedSuffixCylinder",
      "kind": "lean_module",
      "label": "Erdos249257.SelectedSuffixCylinder",
      "path": "lean/Erdos249257/SelectedSuffixCylinder.lean",
      "role": "Terminally indexed selected suffix-cylinder propagation",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SelectedSuffixCylinder.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SelectedSuffixCylinder.lean"
    },
    {
      "id": "lean-module:Erdos249257.SelectedSuffixCylinderPreFeedback",
      "kind": "lean_module",
      "label": "Erdos249257.SelectedSuffixCylinderPreFeedback",
      "path": "lean/Erdos249257/SelectedSuffixCylinderPreFeedback.lean",
      "role": "Selected suffix-cylinder run through the first feedback row",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SelectedSuffixCylinderPreFeedback.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SelectedSuffixCylinderPreFeedback.lean"
    },
    {
      "id": "lean-module:Erdos249257.SignedQMomentObstruction",
      "kind": "lean_module",
      "label": "Erdos249257.SignedQMomentObstruction",
      "path": "lean/Erdos249257/SignedQMomentObstruction.lean",
      "role": "Finite signed-moment determinant and dyadic-parity substrate",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SignedQMomentObstruction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SignedQMomentObstruction.lean"
    },
    {
      "id": "lean-module:Erdos249257.SquareCRTCube",
      "kind": "lean_module",
      "label": "Erdos249257.SquareCRTCube",
      "path": "lean/Erdos249257/SquareCRTCube.lean",
      "role": "Finite square-CRT correction-suppression mechanism",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SquareCRTCube.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SquareCRTCube.lean"
    },
    {
      "id": "lean-module:Erdos249257.SquaredMersenneDiagonalEnclosure",
      "kind": "lean_module",
      "label": "Erdos249257.SquaredMersenneDiagonalEnclosure",
      "path": "lean/Erdos249257/SquaredMersenneDiagonalEnclosure.lean",
      "role": "Sharp squared-Mersenne diagonal enclosure",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SquaredMersenneDiagonalEnclosure.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SquaredMersenneDiagonalEnclosure.lean"
    },
    {
      "id": "lean-module:Erdos249257.SternBrocotRunGeometry",
      "kind": "lean_module",
      "label": "Erdos249257.SternBrocotRunGeometry",
      "path": "lean/Erdos249257/SternBrocotRunGeometry.lean",
      "role": "Stern-Brocot run geometry",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SternBrocotRunGeometry.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SternBrocotRunGeometry.lean"
    },
    {
      "id": "lean-module:Erdos249257.SublogDivisorCoverage",
      "kind": "lean_module",
      "label": "Erdos249257.SublogDivisorCoverage",
      "path": "lean/Erdos249257/SublogDivisorCoverage.lean",
      "role": "Sublogarithmic divisor-coverage constraint",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SublogDivisorCoverage.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SublogDivisorCoverage.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderBelow",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderBelow",
      "path": "lean/Erdos249257/SuffixCylinderBelow.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderBelow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderBelow.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderCarryPivot",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderCarryPivot",
      "path": "lean/Erdos249257/SuffixCylinderCarryPivot.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderCarryPivot.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderCarryPivot.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderFeedbackFanIn",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderFeedbackFanIn",
      "path": "lean/Erdos249257/SuffixCylinderFeedbackFanIn.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderFeedbackFanIn.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderFeedbackFanIn.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderFiniteGap",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderFiniteGap",
      "path": "lean/Erdos249257/SuffixCylinderFiniteGap.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderFiniteGap.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderFiniteGap.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderFirstFeedback",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderFirstFeedback",
      "path": "lean/Erdos249257/SuffixCylinderFirstFeedback.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderFirstFeedback.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderFirstFeedback.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderGlobalProducer",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderGlobalProducer",
      "path": "lean/Erdos249257/SuffixCylinderGlobalProducer.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderGlobalProducer.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderGlobalProducer.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderInStrip",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderInStrip",
      "path": "lean/Erdos249257/SuffixCylinderInStrip.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderInStrip.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderInStrip.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderProfiledAdjacency",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderProfiledAdjacency",
      "path": "lean/Erdos249257/SuffixCylinderProfiledAdjacency.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledAdjacency.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledAdjacency.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderProfiledAutoStep",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderProfiledAutoStep",
      "path": "lean/Erdos249257/SuffixCylinderProfiledAutoStep.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledAutoStep.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledAutoStep.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderProfiledGap",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderProfiledGap",
      "path": "lean/Erdos249257/SuffixCylinderProfiledGap.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledGap.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledGap.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderProfiledPromotion",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderProfiledPromotion",
      "path": "lean/Erdos249257/SuffixCylinderProfiledPromotion.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledPromotion.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledPromotion.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderProfiledPromotionAdjacency",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderProfiledPromotionAdjacency",
      "path": "lean/Erdos249257/SuffixCylinderProfiledPromotionAdjacency.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledPromotionAdjacency.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledPromotionAdjacency.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderProfiledSwallow",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderProfiledSwallow",
      "path": "lean/Erdos249257/SuffixCylinderProfiledSwallow.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledSwallow.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderProfiledSwallow.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderPromotion",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderPromotion",
      "path": "lean/Erdos249257/SuffixCylinderPromotion.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderPromotion.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderPromotion.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderStage51",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderStage51",
      "path": "lean/Erdos249257/SuffixCylinderStage51.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderStage51.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderStage51.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderTerminalOnlyBridge",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderTerminalOnlyBridge",
      "path": "lean/Erdos249257/SuffixCylinderTerminalOnlyBridge.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderTerminalOnlyBridge.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderTerminalOnlyBridge.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderThreshold",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderThreshold",
      "path": "lean/Erdos249257/SuffixCylinderThreshold.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderThreshold.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderThreshold.lean"
    },
    {
      "id": "lean-module:Erdos249257.SuffixCylinderTwoSheet",
      "kind": "lean_module",
      "label": "Erdos249257.SuffixCylinderTwoSheet",
      "path": "lean/Erdos249257/SuffixCylinderTwoSheet.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderTwoSheet.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SuffixCylinderTwoSheet.lean"
    },
    {
      "id": "lean-module:Erdos249257.SupportDilationDifferences",
      "kind": "lean_module",
      "label": "Erdos249257.SupportDilationDifferences",
      "path": "lean/Erdos249257/SupportDilationDifferences.lean",
      "role": "Finite support-dilation difference identities",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SupportDilationDifferences.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SupportDilationDifferences.lean"
    },
    {
      "id": "lean-module:Erdos249257.SupportSunflowerDichotomy",
      "kind": "lean_module",
      "label": "Erdos249257.SupportSunflowerDichotomy",
      "path": "lean/Erdos249257/SupportSunflowerDichotomy.lean",
      "role": "Conditional orthogonal-petal support reduction",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SupportSunflowerDichotomy.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/SupportSunflowerDichotomy.lean"
    },
    {
      "id": "lean-module:Erdos249257.TerminalOnlyCofinal",
      "kind": "lean_module",
      "label": "Erdos249257.TerminalOnlyCofinal",
      "path": "lean/Erdos249257/TerminalOnlyCofinal.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TerminalOnlyCofinal.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TerminalOnlyCofinal.lean"
    },
    {
      "id": "lean-module:Erdos249257.TerminalOnlyScaledVanishing",
      "kind": "lean_module",
      "label": "Erdos249257.TerminalOnlyScaledVanishing",
      "path": "lean/Erdos249257/TerminalOnlyScaledVanishing.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TerminalOnlyScaledVanishing.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TerminalOnlyScaledVanishing.lean"
    },
    {
      "id": "lean-module:Erdos249257.ThreeTransportBoundary",
      "kind": "lean_module",
      "label": "Erdos249257.ThreeTransportBoundary",
      "path": "lean/Erdos249257/ThreeTransportBoundary.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ThreeTransportBoundary.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/ThreeTransportBoundary.lean"
    },
    {
      "id": "lean-module:Erdos249257.Totient827ParitySocketCeiling",
      "kind": "lean_module",
      "label": "Erdos249257.Totient827ParitySocketCeiling",
      "path": "lean/Erdos249257/Totient827ParitySocketCeiling.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/Totient827ParitySocketCeiling.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/Totient827ParitySocketCeiling.lean"
    },
    {
      "id": "lean-module:Erdos249257.TotientActualLcmOrbitArithmetic",
      "kind": "lean_module",
      "label": "Erdos249257.TotientActualLcmOrbitArithmetic",
      "path": "lean/Erdos249257/TotientActualLcmOrbitArithmetic.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitArithmetic.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitArithmetic.lean"
    },
    {
      "id": "lean-module:Erdos249257.TotientActualLcmOrbitNonintegrality",
      "kind": "lean_module",
      "label": "Erdos249257.TotientActualLcmOrbitNonintegrality",
      "path": "lean/Erdos249257/TotientActualLcmOrbitNonintegrality.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitNonintegrality.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitNonintegrality.lean"
    },
    {
      "id": "lean-module:Erdos249257.TotientActualLcmOrbitSeparation",
      "kind": "lean_module",
      "label": "Erdos249257.TotientActualLcmOrbitSeparation",
      "path": "lean/Erdos249257/TotientActualLcmOrbitSeparation.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitSeparation.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitSeparation.lean"
    },
    {
      "id": "lean-module:Erdos249257.TotientActualLcmOrbitSign",
      "kind": "lean_module",
      "label": "Erdos249257.TotientActualLcmOrbitSign",
      "path": "lean/Erdos249257/TotientActualLcmOrbitSign.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitSign.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmOrbitSign.lean"
    },
    {
      "id": "lean-module:Erdos249257.TotientActualLcmShortKill",
      "kind": "lean_module",
      "label": "Erdos249257.TotientActualLcmShortKill",
      "path": "lean/Erdos249257/TotientActualLcmShortKill.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmShortKill.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmShortKill.lean"
    },
    {
      "id": "lean-module:Erdos249257.TotientActualLcmTopEdgeStaircase",
      "kind": "lean_module",
      "label": "Erdos249257.TotientActualLcmTopEdgeStaircase",
      "path": "lean/Erdos249257/TotientActualLcmTopEdgeStaircase.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmTopEdgeStaircase.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/Erdos249257/TotientActualLcmTopEdgeStaircase.lean"
    },
    {
      "id": "lean-module:Erdos249257.TotientCarryKernelRigidity",
      "kind": "lean_module",
      "label": "Erdos249257.TotientCarryKernelRigidity",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/PrimitiveRecordBoundary.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/ReciprocalProductAmplification.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/RecordDivisibility.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/RecordDivisibility.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/SubcriticalRecordBoundary.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/UncentredSeries.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/UncentredSeries.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/WindowIncidence.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR11/WindowIncidence.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateDefect.lean",
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateDifferenceLimits.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateFiniteDifference.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateFiniteDifference.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateNormalisation.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRatePositiveRationalProfile.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateProductAsymptotic.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateProductEndpoint.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateQuotientBounded.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateQuotientIncrement.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateQuotientIncrement.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateRationalProfile.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateRationalProfile.lean"
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      "label": "ErdosProblems.Erdos243.PaperCompleteR20.CubicRateResidualConstant",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateResidualConstant.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateResidualConstant.lean"
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      "label": "ErdosProblems.Erdos243.PaperCompleteR20.CubicRateResidualStep",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateResidualStep.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateResidualStep.lean"
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      "label": "ErdosProblems.Erdos243.PaperCompleteR20.CubicRateSummableTail",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRateSummableTail.lean",
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicRecoveryAudit.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CubicSquareSpecializationAssembly.lean",
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightAnalytic.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightAnalytic.lean"
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightConstruction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightConstruction.lean"
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      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightCriterion.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightCriterion.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightCriterion.lean"
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      "id": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.CutoffWeightForward",
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      "label": "ErdosProblems.Erdos243.PaperCompleteR20.CutoffWeightForward",
      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightForward.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightForward.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightForward.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.CutoffWeightReverse",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos243.PaperCompleteR20.CutoffWeightReverse",
      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightReverse.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightReverse.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/CutoffWeightReverse.lean"
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      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR20/InclusiveOne.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/InclusiveOne.lean",
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/PowerPersistence.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/PowerPersistence.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/RealCutoffCriterion.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/RealCutoffCriterion.lean"
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      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR20/ScaleTwelve.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/ScaleTwelve.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/ScaleTwelve.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR20/TwoForbiddenWords.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/CubicProfileGcdShape.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/CubicProfileGcdShape.lean"
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      "role": "Lean proof module",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/DoubleLogOrbitBound.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/MaximalGapConstant.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/NegativeMagnitudeExclusions.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/NonintegralRegularRate.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/RecordJumpEnergySeries.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/ReducedStepLocalArithmetic.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/RegularRateExtraction.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/ShiftedSignComparison.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/SlowGrowthProductIncrements.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/SlowNegativePartRecord.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/SquareSpecialisationDedekind.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/SquareSpecialisationUnconditional.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/WindowAvoidance.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR21/WindowAvoidance.lean"
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      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR7/Arithmetic.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR7/Arithmetic.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR7/Arithmetic.lean"
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      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR7/CanonicalState.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR7/CanonicalState.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR7/CanonicalState.lean"
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      "path": "lean/ErdosProblems/Erdos243/PaperCompleteR7/Frontier.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR7/Frontier.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos243/PaperCompleteR7/Frontier.lean"
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/CanonicalDyadicSectionRank.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/CarryDescriptionInformationLoss.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/CarryDescriptionInformationLoss.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/CoprimeLatticeSumsAndLambert.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/DivisorChannelSplitAndSeamDoubling.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/DoublingOrbitTransferAndFullDepthPhase.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/DyadicPrefixTailBound.lean",
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      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/FareyExactRangeAndDenominatorExclusion.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/FirstHarmonicBlockCriteria.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/LcmJumpPositionsAndCentralSlack.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/MersennePrimeSupportAnchors.lean",
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      "label": "ErdosProblems.Erdos249.PaperCompleteR21.NearIntegerIrrationalityCriterion",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/NearIntegerIrrationalityCriterion.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/NearIntegerIrrationalityCriterion.lean"
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/NumeratorPolynomialAndMersenneRemainder.lean",
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      "label": "ErdosProblems.Erdos249.PaperCompleteR21.PenultimateStaircaseAndRankCurvature",
      "path": "lean/ErdosProblems/Erdos249/PaperCompleteR21/PenultimateStaircaseAndRankCurvature.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/PenultimateStaircaseAndRankCurvature.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos249/PaperCompleteR21/PenultimateStaircaseAndRankCurvature.lean"
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      "id": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PeriodMultipleAndSecondDifference",
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BranchCellHorizonExclusions",
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.BranchCellHorizonExclusions",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/BranchCellHorizonExclusions.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/BranchCellHorizonExclusions.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/BranchCellHorizonExclusions.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary",
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/CentredCompletionAndDecisionBoundary.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/CentredCompletionAndDecisionBoundary.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/CentredCompletionAndDecisionBoundary.lean"
    },
    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CompatibleFiniteRowFamily",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.CompatibleFiniteRowFamily",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/CompatibleFiniteRowFamily.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/CompatibleFiniteRowFamily.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/CompatibleFiniteRowFamily.lean"
    },
    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CriticalDyadicBandCollapse",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.CriticalDyadicBandCollapse",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/CriticalDyadicBandCollapse.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/CriticalDyadicBandCollapse.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/CriticalDyadicBandCollapse.lean"
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.DenominatorBudget",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.DenominatorBudget",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/DenominatorBudget.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/DenominatorBudget.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/DenominatorBudget.lean"
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.DyadicBandAndTwoSidedBounds",
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.DyadicBandAndTwoSidedBounds",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/DyadicBandAndTwoSidedBounds.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/DyadicBandAndTwoSidedBounds.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/DyadicBandAndTwoSidedBounds.lean"
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      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.EventualNonnegativeMargin",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/EventualNonnegativeMargin.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/EventualNonnegativeMargin.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/EventualNonnegativeMargin.lean"
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      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/ExactRowDichotomyCountermodels.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ExactRowDichotomyCountermodels.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ExactRowDichotomyCountermodels.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FeedbackRowStripWitnessAllDepths",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.FeedbackRowStripWitnessAllDepths",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/FeedbackRowStripWitnessAllDepths.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/FeedbackRowStripWitnessAllDepths.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/FeedbackRowStripWitnessAllDepths.lean"
    },
    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FiniteFamilyCoverCost",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.FiniteFamilyCoverCost",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/FiniteFamilyCoverCost.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/FiniteFamilyCoverCost.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/FiniteFamilyCoverCost.lean"
    },
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/GreedyGapCriteria.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/GreedyGapCriteria.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/GreedyGapCriteria.lean"
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.GreedyOrbitNoTies",
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/GreedyOrbitNoTies.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/GreedyOrbitNoTies.lean"
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/LinearChannelAndMiddleCellExclusion.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/LinearChannelAndMiddleCellExclusion.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/LinearChannelAndMiddleCellExclusion.lean"
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    {
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/LogarithmicInitialInterval.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/LogarithmicInitialInterval.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/LogarithmicInitialInterval.lean"
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneChannelSurvivalAllHeights",
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.MersenneChannelSurvivalAllHeights",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/MersenneChannelSurvivalAllHeights.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/MersenneChannelSurvivalAllHeights.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/MersenneChannelSurvivalAllHeights.lean"
    },
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences",
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences",
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      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/MersenneQuotientRowRecurrences.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/MersenneQuotientRowRecurrences.lean"
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/MobiusSignAndFiniteCertificates.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/MobiusSignAndFiniteCertificates.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/MobiusSignAndFiniteCertificates.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OddReciprocalDenominators",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.OddReciprocalDenominators",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/OddReciprocalDenominators.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/OddReciprocalDenominators.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/OddReciprocalDenominators.lean"
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    {
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      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.OneSidedCertificateHierarchy",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/OneSidedCertificateHierarchy.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/OneSidedCertificateHierarchy.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/OneSidedCertificateHierarchy.lean"
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      "kind": "lean_module",
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      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/PostTakeBandLocalisation.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/PostTakeBandLocalisation.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/PostTakeBandLocalisation.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/ResetSqrtEscapeHalfMembership.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ResetSqrtEscapeHalfMembership.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ResetSqrtEscapeHalfMembership.lean"
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.ResidueClassSupport",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/ResidueClassSupport.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ResidueClassSupport.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ResidueClassSupport.lean"
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      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/ScalarLocalisationHeightObstruction.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ScalarLocalisationHeightObstruction.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ScalarLocalisationHeightObstruction.lean"
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      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamEscapeAndTerminalStrip",
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.SeamEscapeAndTerminalStrip",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamEscapeAndTerminalStrip.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamEscapeAndTerminalStrip.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamEscapeAndTerminalStrip.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamPrefixStabilityLimit",
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      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamPrefixStabilityLimit.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamPrefixStabilityLimit.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamPrefixStabilityLimit.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamQuotientDeficitLimit",
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.SeamQuotientDeficitLimit",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamQuotientDeficitLimit.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamQuotientDeficitLimit.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamQuotientDeficitLimit.lean"
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    {
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamRowGapAndCarry.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamRowGapAndCarry.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SeamRowGapAndCarry.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SharedPrefixFamiliesAndMeasureDichotomy",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.SharedPrefixFamiliesAndMeasureDichotomy",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SharedPrefixFamiliesAndMeasureDichotomy.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SharedPrefixFamiliesAndMeasureDichotomy.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SharedPrefixFamiliesAndMeasureDichotomy.lean"
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    {
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      "label": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/ShortWindowDivisorPhase.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ShortWindowDivisorPhase.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/ShortWindowDivisorPhase.lean"
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    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SkipSafetyAndDivisorZeroRuns",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.SkipSafetyAndDivisorZeroRuns",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SkipSafetyAndDivisorZeroRuns.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SkipSafetyAndDivisorZeroRuns.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SkipSafetyAndDivisorZeroRuns.lean"
    },
    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquareDepthAndHalfMembershipEquivalences",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.SquareDepthAndHalfMembershipEquivalences",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SquareDepthAndHalfMembershipEquivalences.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SquareDepthAndHalfMembershipEquivalences.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SquareDepthAndHalfMembershipEquivalences.lean"
    },
    {
      "id": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquarefreeSupportEngineCeiling",
      "kind": "lean_module",
      "label": "ErdosProblems.Erdos257.PaperCompleteR21.SquarefreeSupportEngineCeiling",
      "path": "lean/ErdosProblems/Erdos257/PaperCompleteR21/SquarefreeSupportEngineCeiling.lean",
      "role": "Lean proof module",
      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SquarefreeSupportEngineCeiling.lean",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCompleteR21/SquarefreeSupportEngineCeiling.lean"
    },
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCorrespondenceAuditAdditiveWave7.lean",
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      "href": "https://github.com/wcook04/plectis-erdos/blob/main/lean/ErdosProblems/Erdos257/PaperCorrespondenceAuditAdditiveWave8.lean",
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      "id": "paper:erdos-251-prime-gap-dyadic-series",
      "kind": "paper",
      "label": "Sparse Congruence-Preserving Perturbations of Dyadic Series",
      "subject": "Erdős #251",
      "form": "Problem note",
      "href": "papers/erdos-251-prime-gap-dyadic-series.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/251/erdos-251-prime-gap-dyadic-series.tex"
    },
    {
      "id": "paper:erdos-257-mersenne-support-subseries",
      "kind": "paper",
      "label": "Irrationality criteria for Lambert subseries",
      "subject": "Erdős #257",
      "form": "Problem note",
      "href": "papers/erdos-257-mersenne-support-subseries.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/257/erdos-257-mersenne-support-subseries.tex"
    },
    {
      "id": "paper:erdos-269-three-prime-running-lcm",
      "kind": "paper",
      "label": "Distinct running least common multiples",
      "subject": "Erdős #269",
      "form": "Problem note",
      "href": "papers/erdos-269-three-prime-running-lcm.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/269/erdos-269-three-prime-running-lcm.tex"
    },
    {
      "id": "paper:erdos-68-factorial-denominator-irrationality",
      "kind": "paper",
      "label": "Integer Linear Forms for a Factorial Reciprocal Series",
      "subject": "Erdős #68",
      "form": "Problem note",
      "href": "papers/erdos-68-factorial-denominator-irrationality.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/68/erdos-68-factorial-denominator-irrationality.tex"
    },
    {
      "id": "paper:erdos1041-lemniscate-reasoning-surface",
      "kind": "paper",
      "label": "Paths in Polynomial Lemniscates: A Degree-Seven Counterexample and Radial Connections",
      "subject": "Erdős #1041",
      "form": "Reasoning surface",
      "href": "papers/erdos1041-lemniscate-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/1041/erdos1041-lemniscate-reasoning-surface.tex"
    },
    {
      "id": "paper:erdos1049-rational-base-lambert-reasoning-surface",
      "kind": "paper",
      "label": "Geometric Moments and Rational Lambert Values: Proofs and Further Results",
      "subject": "Erdős #1049",
      "form": "Reasoning surface",
      "href": "papers/erdos1049-rational-base-lambert-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/1049/erdos1049-rational-base-lambert-reasoning-surface.tex"
    },
    {
      "id": "paper:erdos243-reciprocal-tail-reasoning-surface",
      "kind": "paper",
      "label": "Reciprocal Sums and the Sylvester Recurrence: Further Results and Proofs",
      "subject": "Erdős #243",
      "form": "Reasoning surface",
      "href": "papers/erdos243-reciprocal-tail-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/243/erdos243-reciprocal-tail-reasoning-surface.tex"
    },
    {
      "id": "paper:erdos249-totient-reasoning-surface",
      "kind": "paper",
      "label": "The Binary Totient Series",
      "subject": "Erdős #249",
      "form": "Reasoning surface",
      "href": "papers/erdos249-totient-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/249/erdos249-totient-reasoning-surface.tex"
    },
    {
      "id": "paper:erdos251-prime-gap-reasoning-surface",
      "kind": "paper",
      "label": "Prime-Gap Dyadic Series: Perturbations, Exact Criteria and Certificates",
      "subject": "Erdős #251",
      "form": "Reasoning surface",
      "href": "papers/erdos251-prime-gap-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/251/erdos251-prime-gap-reasoning-surface.tex"
    },
    {
      "id": "paper:erdos257-expository-sums-never-fractions",
      "kind": "paper",
      "label": "Why certain sums of 1/(2^n-1) are irrational",
      "subject": "Erdős #257",
      "form": "Expository paper",
      "href": "papers/erdos257-expository-sums-never-fractions.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/257/erdos257-expository-sums-never-fractions.tex",
      "side": "expository"
    },
    {
      "id": "paper:erdos257-mersenne-reasoning-surface",
      "kind": "paper",
      "label": "Reciprocal Mersenne Subseries",
      "subject": "Erdős #257",
      "form": "Reasoning surface",
      "href": "papers/erdos257-mersenne-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/257/erdos257-mersenne-reasoning-surface.tex"
    },
    {
      "id": "paper:erdos269-running-lcm-reasoning-surface",
      "kind": "paper",
      "label": "Running least common multiples: distinct values and multiplicities",
      "subject": "Erdős #269",
      "form": "Reasoning surface",
      "href": "papers/erdos269-running-lcm-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/269/erdos269-running-lcm-reasoning-surface.tex"
    },
    {
      "id": "paper:erdos68-factorial-reasoning-surface",
      "kind": "paper",
      "label": "Factorial Linear Forms and Denominators: Detailed Proofs and Rationality Criteria",
      "subject": "Erdős #68",
      "form": "Reasoning surface",
      "href": "papers/erdos68-factorial-reasoning-surface.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/68/erdos68-factorial-reasoning-surface.tex"
    },
    {
      "id": "paper:optimal-sparse-perturbations",
      "kind": "paper",
      "label": "Reading Eight Erdős Problems Together",
      "subject": "Eight Erdős problems read together",
      "form": "Cross-problem paper",
      "href": "papers/optimal-sparse-perturbations.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/synthesis/optimal-sparse-perturbations.tex"
    },
    {
      "id": "paper:plectis-public-system",
      "kind": "paper",
      "label": "Plectis: What a Stranger Can Check",
      "subject": "Systems paper",
      "form": "Evidence boundary",
      "href": "papers/plectis-public-system.json",
      "source_github": "https://github.com/wcook04/practical-formal-verification/blob/main/paper/plectis-public-system.tex"
    },
    {
      "id": "paper:writing-a-good-mathematical-paper",
      "kind": "paper",
      "label": "Writing a Good Mathematical Paper",
      "subject": "Exposition method",
      "form": "Compact writing guide",
      "href": "papers/writing-a-good-mathematical-paper.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/exposition/writing-a-good-mathematical-paper.tex"
    },
    {
      "id": "paper:writing-mathematics-from-reviewed-revisions",
      "kind": "paper",
      "label": "Writing Mathematics from the Literature and Reviewed Revisions",
      "subject": "Exposition method",
      "form": "Editorial method companion",
      "href": "papers/writing-mathematics-from-reviewed-revisions.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/paper/exposition/writing-mathematics-from-reviewed-revisions.tex"
    },
    {
      "id": "problem:erdos_1041",
      "kind": "problem",
      "label": "Short connections inside polynomial lemniscates",
      "status": "formal statement refuted",
      "question": "Must two roots of a monic polynomial in the open unit disc be joined by a sub-two-length curve inside its unit lemniscate? Ani’s degree-seven example refutes the exact Formal Conjectures statement; correspondence with the 1958 wording awaits human review.",
      "href": "problems/erdos_1041.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos1041"
    },
    {
      "id": "problem:erdos_1049",
      "kind": "problem",
      "label": "Lambert-type series at rational bases",
      "status": "open",
      "question": "For which rational bases is the corresponding series irrational? The first resistant explicit base is three halves.",
      "href": "problems/erdos_1049.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos1049"
    },
    {
      "id": "problem:erdos_243",
      "kind": "problem",
      "label": "Reciprocal-tail rigidity near the Sylvester recurrence",
      "status": "open",
      "question": "Under a rapid-growth hypothesis on an integer sequence, does rationality of its reciprocal sum force the sequence to satisfy the Sylvester recurrence eventually?",
      "href": "problems/erdos_243.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos243"
    },
    {
      "id": "problem:erdos_249",
      "kind": "problem",
      "label": "The binary totient series",
      "status": "open",
      "question": "Is the binary Lambert series sum phi(n)/2^n irrational?",
      "href": "problems/erdos_249.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos249"
    },
    {
      "id": "problem:erdos_251",
      "kind": "problem",
      "label": "The prime-gap dyadic series",
      "status": "open",
      "question": "Is the dyadic series of consecutive primes irrational? Equivalently, is the corresponding consecutive-prime-gap dyadic series irrational?",
      "href": "problems/erdos_251.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos251"
    },
    {
      "id": "problem:erdos_257",
      "kind": "problem",
      "label": "Reciprocal sums over infinite exponent supports",
      "status": "open",
      "question": "Is the sum of 1/(2^n-1) over every infinite set of positive exponents irrational?",
      "href": "problems/erdos_257.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos257"
    },
    {
      "id": "problem:erdos_269",
      "kind": "problem",
      "label": "Three-prime running least common multiples",
      "status": "open",
      "question": "For a finite set of at least two primes, is the sum of reciprocals of the running least common multiples of the smooth numbers irrational? This library treats the three-prime case.",
      "href": "problems/erdos_269.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos269"
    },
    {
      "id": "problem:erdos_68",
      "kind": "problem",
      "label": "The factorial-denominator series",
      "status": "open",
      "question": "Is the series sum_{n >= 2} 1/(n! - 1) irrational?",
      "href": "problems/erdos_68.json",
      "source_github": "https://github.com/wcook04/plectis-erdos/blob/main/docs/problems.json",
      "source_directory_github": "https://github.com/wcook04/plectis-erdos/tree/main/lean/ErdosProblems/Erdos68"
    },
    {
      "id": "statement:erdos-1041-lemniscate-newton-flow#lem:two-sheet-bottleneck",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos1041/Counterexample/HausdorffLength.lean#L187",
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      "label": "Lemma 2.1",
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      "id": "statement:erdos-1041-lemniscate-newton-flow#res:ani-degree-seven-counterexample",
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          "name": "Erdos1041.Counterexample.erdos1041_hausdorff_negation",
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          "name": "Erdos1041.Counterexample.erdos1041_hausdorff_answer_false",
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      "page": "2",
      "evidence_record": "https://github.com/wcook04/plectis-erdos/blob/main/evidence/erdos-1041-lemniscate-newton-flow.md#res-ani-degree-seven-counterexample",
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      "label": "Theorem 1.2 (ani’s degree-seven example)",
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    {
      "id": "statement:erdos-1041-lemniscate-newton-flow#res:critical-value-separation",
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      "problem_id": "erdos_1041",
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        {
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos1041/PaperCompleteR21/CriticalValueSeparationTransport.lean#L179",
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      "named_inputs": [
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      "page": "10",
      "evidence_record": "https://github.com/wcook04/plectis-erdos/blob/main/evidence/erdos-1041-lemniscate-newton-flow.md#res-critical-value-separation",
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      "label": "Remark 5.1 (unformalised isolated-value assertion)",
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    {
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      "side": "short",
      "lean_status": "modulo_named_input",
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      "palomar_status": "not_applicable",
      "declarations": [
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          "name": "ErdosProblems.Erdos1041.PaperCompleteR21.discSep_uniform_radius",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos1041/PaperCompleteR21/CriticalValueSeparationTransport.lean#L702",
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          "name": "ErdosProblems.Erdos1041.PaperCompleteR21.discSep_cubic_six_fifths",
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        {
          "name": "ErdosProblems.Erdos1041.PaperCompleteR21.discSepCoefficient_lt_two",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos1041/PaperCompleteR21/CriticalValueSeparationTransport.lean#L645",
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          "name": "ErdosProblems.Erdos1041.PaperCompleteR21.discSepCoefficient_three_six_fifths",
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          "name": "ErdosProblems.Erdos1041.PaperCompleteR21.SeparationParent.separation_parent",
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          "name": "ErdosProblems.Erdos249.PaperCompleteR21.irrational_of_powerTwo_postJump_slack_supply",
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        {
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        {
          "name": "ErdosProblems.Erdos249.PaperCompleteR21.paperTeChain_item_one_unfolded",
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        {
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        {
          "name": "ErdosProblems.Erdos249.PaperCompleteR21.teChain_item_three_unfolded",
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        {
          "name": "ErdosProblems.Erdos249.PaperCompleteR21.teChain_item_four_unfolded",
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          "name": "ErdosProblems.Erdos249.PaperCompleteR21.teChain_item_five_unfolded",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos249/PaperCompleteR21/TopEdgeCorridorAndSeparation.lean#L142",
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          "name": "ErdosProblems.Erdos249.PaperCompleteR21.paperTeChain_five_sufficient_for_irrationality",
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        {
          "name": "ErdosProblems.Erdos249.PaperCompleteR21.paperTeChain_first_four_imply_topEdgeSupply",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos249/PaperCompleteR21/TopEdgeChainPaperBand.lean#L233",
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        {
          "name": "ErdosProblems.Erdos249.PaperCompleteR21.paperTeChain_relations",
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        {
          "name": "ErdosProblems.Erdos249.PaperCompleteR21.topEdgeResidueGap_or_of_paperAdjacentSuffixMidband",
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        {
          "name": "ErdosProblems.Erdos249.PaperCompleteR21.powerTwoActualLcmTopEdgeResidueGapSupply_of_paperAdjacentSuffixMidband",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos249/PaperCompleteR21/TopEdgeChainPaperBand.lean#L179",
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        {
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          "name": "ErdosProblems.Erdos249.PaperCompleteR21.paperAdjacentSuffixMidbandSupply_of_oddGuardTopEdgeHalfWordBand",
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          "name": "ErdosProblems.Erdos249.PaperCompleteR21.paperAdjacentSuffixMidbandSupply_of_flexibleActualTopEdgeMagnitude",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos249/PaperCompleteR21/TopEdgeChainPaperBand.lean#L204",
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          "name": "ErdosProblems.Erdos249.PaperCompleteR21.paperAdjacentSuffixMidbandSupply_of_adjacentSuffixMidband",
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          "name": "ErdosProblems.Erdos249.PaperCompleteR21.cyclotomic_four_eval",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/Erdos249257/HalfTrappingReturnCarry.lean#L42",
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          "name": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase.iLeast_mem_Icc",
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          "name": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase.iLeast_congr",
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        {
          "name": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase.theta_eq_Psi",
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          "name": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase.Psi_eq_of_residues_eq",
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          "name": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase.theta_one_one",
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        {
          "name": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase.theta_one_three",
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        {
          "name": "ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase.residue_cutoff_reading_fails",
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      "label": "Lemma 11.2 (Divisor-residue form of the short-window phase)",
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        {
          "name": "Erdos249257.positiveMersenneSupportValue_insert",
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          "name": "Erdos249257.HalfUpperResetCriticalBand.dyadicBandEscape_iff_exists_critical",
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          "name": "ErdosProblems.Erdos257.PaperCompleteR21.paper_rowLower_existsUnique",
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      "paper_label": "thm:full-support",
      "label": "Theorem 5.4 (Full-support irrationality, unconditional, every base b ≥ 2)",
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      "label": "Theorem 6.14 (Erdős–Borwein full-support irrationality, unconditional)",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/ErdosProblems/Erdos257/PaperCompleteR20/AchievementGeometry.lean#L40",
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      "label": "Theorem 1.8 (Achievement-set geometry)",
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    {
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          "name": "Erdos249257.mem_mersenneAchievementSet_iff_greedy_survival",
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      "label": "Theorem 6.35 (Greedy survival and membership)",
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          "name": "Erdos249257.greedy_survives_of_mem_mersenneAchievementSet",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/Erdos249257/GreedyAchievementSet.lean#L1375",
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          "name": "Erdos249257.mem_mersenneAchievementSet_of_greedy_survival",
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          "name": "Erdos249257.half_mem_mersenneAchievementSet_iff_greedySkippedSupport_infinite",
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          "href": "https://github.com/wcook04/plectis-erdos/blob/436f55ebdafa67e4af0fff79f621c13f2ded12bf/lean/Erdos249257/GreedyAchievementSet.lean#L2583",
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    {
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      "source": "claim:mersenne_tail_atom_boundary",
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    {
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    {
      "source": "claim:newton_ray_separation_consumer",
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    {
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      "relation": "same_lean_declaration",
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    },
    {
      "source": "claim:nonintegral_regular_rate_irrationality",
      "relation": "supported_by",
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      "source": "claim:parity_socket_obstruction",
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    {
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    {
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    },
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      "source": "claim:power_two_bit_lift",
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    {
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    {
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    {
      "source": "claim:producer_carry_future_tail_socket",
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    {
      "source": "claim:quarter_band_endpoint_cells",
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      "target": "lean-module:Erdos249257.HalfCylinderQuarterBandEndpoints",
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    {
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    {
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    {
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    {
      "source": "claim:reciprocal_mass_bound",
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    {
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    },
    {
      "source": "claim:reciprocal_summable_support",
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      "target": "lean-module:Erdos249257.AllBaseReciprocalSupportIrrationality",
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    {
      "source": "claim:reset_deficit_escape_geometry",
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    {
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    {
      "source": "claim:rewind_seam_operational_bridge",
      "relation": "supported_by",
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    },
    {
      "source": "claim:seam_producer_carry_alignment",
      "relation": "supported_by",
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    {
      "source": "claim:selected_half_carry_window_compactness",
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    {
      "source": "claim:selected_suffix_cylinder_propagation",
      "relation": "same_lean_declaration",
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    },
    {
      "source": "claim:selected_suffix_cylinder_propagation",
      "relation": "supported_by",
      "target": "lean-module:Erdos249257.SelectedSuffixCylinder",
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    },
    {
      "source": "claim:selected_suffix_cylinder_propagation",
      "relation": "supported_by",
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      "target": "statement:erdos-251-prime-gap-dyadic-series#res:irr-equivalence"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:signedwindow"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:sparserationalisation"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:true-tail"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:truncation"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#res:cylinderhalf"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#res:general-repair"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#res:mixed-supports"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#res:one-over-twenty-one-frontier"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#res:period"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#res:reciprocal-support"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#res:weighted-support"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-257-mersenne-support-subseries#thm:variable-fractional-cover"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:actual-orbit"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:admissible-modular-minors"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:cell"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:consumer"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:denominator-reduction"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:dyadic-alphabet"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:exact-onset"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:fibre-prop"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:finite-cut-rank"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:infinite-rank"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:lcm"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-269-three-prime-running-lcm#res:windowconsumer"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-68-factorial-denominator-irrationality#res:divisor-channel-coordinates"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos-68-factorial-denominator-irrationality#res:finite-channel-moment-certificate"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#cor:collinear-erdos-1041"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#lem:cubic-safe-root-spoke"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#prop:primitive-quintic-two-tail-energy-selector"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#prop:sharp-collinear-chebyshev-comparator"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:circle-slice-packing"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:complementary-binomial-chords"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-proximity"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-value-budget"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:degree-three"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:fp-weighted-all-degree"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:locus"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:one-root-gamma-false"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:orlicz-currency"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:ray"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:reflected-critical-value"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:sep-or-false"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:straight-no-go"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:trinomial-all-degree"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:two-nearest-roots"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:value"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#thm:primitive-quintic-two-tail"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#thm:sharp-collinear-diameter"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#thm:translated-cubic-quotient-fibres"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:cor:no-decay-below-square"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:cor:rational-base-measure"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:prop:rogers-factorisation"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:31over4"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:allrowinitial"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:archcap"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:boundedfibre"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:chargeceilings"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:commonmult"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:content"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:corridorbound"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:cyclounit"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:endpoints"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:exp"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:finite-pencil"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:forcing"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:jetkernel"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:nocorridor"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:nomahler"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:nomult"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:omega-indicator"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:pade"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:plucker-collapse"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:powerbracket"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:rankfortyone"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:region"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:scalar"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:sevenhalves"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:sharpgaps"
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    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:sourceheight"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:tail-lattice"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:tailrec"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:zudilin-sharp-qorder"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:thm:geometric-universality"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:thm:sharp-fixed-base"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#res:bottomjet"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos1049-rational-base-lambert-reasoning-surface#res:boundedfibre"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:absorb"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:arithmeticrecord"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:barrier"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:bounded"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:classicalhalfspace"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:constant"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:coprimalitycap"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:cor"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:criticalrate"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:crt"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:cubicexclusion"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:cubicrate"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:curvature"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:defect"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:descent"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:energycriterion"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:epochenergy"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:eventual"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:extraction"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:frontier"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gapconstant"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gcdshape"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gcdsparse"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gcdstab"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:loglogboundary"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:mass"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:modseven"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:oddpowersupply"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:oldmodulussaturation"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:onethreshold"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:periodic"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:periodicobstruction"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:powerpersistence"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:recordamplified"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:recorddichotomy"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:reduced"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:reduciblecase"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:residue"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:scale"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:scaletwelve"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:secondorder"
    },
    {
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:iffs"
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:lambertengine"
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:mobsq"
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:pillai"
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:route4"
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:shift"
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:sign"
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:sufficient-accumulated-residue-condition"
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:sufficient-extension"
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      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:sufficient-extension-2"
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:sufficient-extension-3"
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#prop:te-chain"
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:certificate-four-tail-combination"
    },
    {
      "source": "integration:comparator",
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    },
    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:denom"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:denom-record"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:denomcoprime"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:denominators-mobius-sums"
    },
    {
      "source": "integration:comparator",
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    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:diagonal-certificate-table"
    },
    {
      "source": "integration:comparator",
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      "source": "integration:comparator",
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    },
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      "source": "integration:comparator",
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    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:fixed-farey-bound"
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    {
      "source": "integration:comparator",
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      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos249-totient-reasoning-surface#thm:one-common-certificate-sixteen-shifts"
    },
    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    },
    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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    {
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "source": "integration:comparator",
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      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:telescope"
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:true-tail"
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#cor:cd-remaining"
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#cor:mersenne-height"
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#cor:negative-mobius-overshoot"
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    {
      "source": "integration:comparator",
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:collapse-mech"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:denominator-survival"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:eventually-right-impossible"
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    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:fatal-gap-exclusion"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:gap-mass-summability"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:half-divisor-unit-drop"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:half-endpoint-kills"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:largest-false-rank-algebra"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:linear-channel-nogo"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:mersenne-tail-weight"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:mixed-prime-power-layer"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:no-ties"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:odometer"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:reverse-carry-word"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:scalar-localization"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:seam-upper-or-middle"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:skipped-endpoint-trichotomy"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:sqrt-witness"
    },
    {
      "source": "integration:comparator",
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      "target": "statement:erdos257-mersenne-reasoning-surface#lem:sqwitness"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:straddle-agrees-greedy"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:tail-transfer"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:tr-mod12"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:tr-parity"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:257-logarithmic-initial-interval"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:2adic-nogo"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:achievement-set-topology"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:canon"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:carry-survivor-extinction"
    },
    {
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      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-cancellation"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-dichotomy"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-escape-endpoint"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-orbit"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-tail-bound"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:all-scale-lattice"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:cell"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:consumer"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:count"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:drop"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:dyadic-alphabet"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:exact-denominator"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:fibre"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:finite-cut-rank"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:fixed-base-recoding"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:infinite-rank"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:jump-constrained-bound"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:lcm"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:literal-triangle"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:no-bounded-length"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:pinning"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:rank"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:residue-limit"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:short"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:strip-decomposition"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:tails-equivalence"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:two-prime-rank"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:uniform-rank"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:weighted-shift-identity"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos269-running-lcm-reasoning-surface#long269:res:window-growth"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:bandbreakpoint"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:carry-equivalence"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:channel-radius"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:companion-orbit"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:gap-gcd"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:global-residue"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:lcm-growth"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:lower-escape"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:moment-ideal"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:normalform"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:prime-pole"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:product-lcm"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:radius-constant"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:residual-transparency"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:segment"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:shift-family"
    },
    {
      "source": "integration:comparator",
      "relation": "replayed",
      "target": "statement:erdos68-factorial-reasoning-surface#long68:res:translator"
    },
    {
      "source": "integration:comparator",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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      "target": "statement:erdos-1049-rational-base-lambert#prop:weight-factorisation"
    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
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    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    {
      "source": "integration:palomar",
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    },
    {
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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      "target": "statement:erdos-249-binary-totient-series#res:rankonefloor"
    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
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      "target": "statement:erdos-249-binary-totient-series#thm:kkernelrank"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:escape-irrational"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:gap-nonperiodic"
    },
    {
      "source": "integration:palomar",
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    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:irr-equivalence"
    },
    {
      "source": "integration:palomar",
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      "target": "statement:erdos-251-prime-gap-dyadic-series#res:signedwindow"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
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    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:true-tail"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-251-prime-gap-dyadic-series#res:truncation"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-257-mersenne-support-subseries#res:cylinderhalf"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-257-mersenne-support-subseries#res:general-repair"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-257-mersenne-support-subseries#res:mixed-supports"
    },
    {
      "source": "integration:palomar",
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      "target": "statement:erdos-257-mersenne-support-subseries#res:one-over-twenty-one-frontier"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-257-mersenne-support-subseries#res:period"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-257-mersenne-support-subseries#res:reciprocal-support"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-257-mersenne-support-subseries#res:weighted-support"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-257-mersenne-support-subseries#thm:variable-fractional-cover"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:actual-orbit"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:admissible-modular-minors"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:cell"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:consumer"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:denominator-reduction"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:dyadic-alphabet"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:exact-onset"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:fibre-prop"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:finite-cut-rank"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:infinite-rank"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:lcm"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-269-three-prime-running-lcm#res:windowconsumer"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-68-factorial-denominator-irrationality#res:divisor-channel-coordinates"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos-68-factorial-denominator-irrationality#res:finite-channel-moment-certificate"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#cor:collinear-erdos-1041"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#lem:cubic-safe-root-spoke"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#prop:primitive-quintic-two-tail-energy-selector"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#prop:sharp-collinear-chebyshev-comparator"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:circle-slice-packing"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:complementary-binomial-chords"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-proximity"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-value-budget"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:degree-three"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:fp-weighted-all-degree"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:locus"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:one-root-gamma-false"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:orlicz-currency"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:ray"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:reflected-critical-value"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:sep-or-false"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:straight-no-go"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:trinomial-all-degree"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:two-nearest-roots"
    },
    {
      "source": "integration:palomar",
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      "target": "statement:erdos1041-lemniscate-reasoning-surface#res:value"
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    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:fixed-farey-bound"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:gamma"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:hgap-norm"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:hgap-real"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:hgap-subset"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:lacunary"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
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    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:one-common-certificate-sixteen-shifts"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:one-explicit-witness"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:positive-coefficients-numerator-polynomial"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:positivity-remaining-residue-inequality"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:prime-satisfying-stated-cyclotomic-conditions"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:proved-implication"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:proved-implications"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
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    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:rationality-carry-rank-2"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:separation-rational-approximation"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:short-window-examples-through-exponent"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:strict-log-concavity-all-integer"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:sufficient-order-hypothesis-unbounded-prime"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:two-adic-congruence-that-does"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:unbounded-prime-support-mersenne-factors"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:uniform-positive-gap-rank-one"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos249-totient-reasoning-surface#thm:values-exponents-one-two"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:abel"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:affinecollapse"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:block"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:boundedperturbation"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:complete-truncation"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:denominatorfloor"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:escape-irrational"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:explicit-remainder"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:finite-smallpair"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:freepair"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:gap-nonperiodic"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:infinite"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:irr-equivalence"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:lcmdiagonal"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:local-targets"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:nonconcentration"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:one-tail-certificate"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:parts"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:polignacfail"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:polynomialcountermodel"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:shiftedcount"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:signedwindow"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:smallpair"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:smallpair-real"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:sparse-nonconcentration"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:sparse-rationalisation"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:telescope"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:res:true-tail"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:boundedpolignac"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:propagate"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:totient"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:truncation"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#cor:257-logarithmic-separation"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#cor:cd-remaining"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#cor:mersenne-height"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#cor:negative-mobius-overshoot"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#cor:tr-half-lcm"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:collapse-mech"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:denominator-survival"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:eventually-right-impossible"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:fatal-gap-exclusion"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:gap-mass-summability"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:half-divisor-unit-drop"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:half-endpoint-kills"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:largest-false-rank-algebra"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:linear-channel-nogo"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:mersenne-tail-weight"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:mixed-prime-power-layer"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:no-ties"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:odometer"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:reverse-carry-word"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:scalar-localization"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:seam-upper-or-middle"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:skipped-endpoint-trichotomy"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:sqrt-witness"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:sqwitness"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:straddle-agrees-greedy"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:tail-transfer"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:tr-mod12"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#lem:tr-parity"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:257-logarithmic-initial-interval"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:2adic-nogo"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:achievement-set-topology"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:canon"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:carry-survivor-extinction"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:collapse"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:collapsed-list"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:cpgs-equiv"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:critical-band-index"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:exact-lebesgue-measure-dichotomy"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:exponent-gap"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:finite-approximations-without-compatibility"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:finite-boolSupport-and-onesided"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:finite-state-nogo"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:mobius-nogo"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:one-orbit"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:squarefree"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:strip-equiv"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:unsafe-middle-range-exactly-three"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#prop:upper-unconditional"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c1"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c10"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c11"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c12"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c14"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c15"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c19"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c2"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c20"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c3"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c4"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c6"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c6a"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c6b"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c7"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c8"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c9"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-bridge"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-cross2"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-mob"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-rank2"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-t7"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i10"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i11a"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i11b"
    },
    {
      "source": "integration:palomar",
      "relation": "holds_prepared",
      "target": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i11c"
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    {
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos243",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos243",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos243",
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      "relation": "imports",
      "target": "lean-module:Erdos249257.CarrySurvivorExtinction"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "target": "lean-module:Erdos249257.CertificateKernel"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "target": "lean-module:Erdos249257.GapFareyBound"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GeneralIrrationalityCriteriaAndGapBounds"
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertSigmaRungAndNesterenko"
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LcmJumpPositionsAndCentralSlack"
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MobiusMersenneLadderLogConcavity"
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NumeratorPolynomialAndMersenneRemainder"
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PenultimateStaircaseAndRankCurvature"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PeriodMultipleAndSecondDifference"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PillaiGcdExpectation"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.QZetaAnchor"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.RationalTailPeriodWitnesses"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ScalarLocalisationAndInversePhaseGauge"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ShortWindowSupplyAndSixteenShifts"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SimultaneousShiftCertificateDepth"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquareBlockBinaryDilationCountermodel"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquaredMersenneDivisorIdentities"
    },
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SternBrocotStoppingRecursion"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TailCarryPeriodAndRankFloor"
    },
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TemperedOrbitAndSquaredMersenneTail"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeChainPaperBand"
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    },
    {
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    {
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseCertificateFailure"
    },
    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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    {
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    {
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    {
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
      "relation": "imports",
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    },
    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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    },
    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos249",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR21.PerturbedPrimePositions"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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    },
    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos251",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:Erdos249257.SuffixCylinderTerminalOnlyBridge"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BalancedPulseFanOutCount"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.EventualNonnegativeMargin"
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FeedbackRowStripWitnessAllDepths"
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria"
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyOrbitNoTies"
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    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion"
    },
    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval"
    },
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      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneChannelSurvivalAllHeights"
    },
    {
      "source": "lean-module:ErdosProblems.ArgumentGraph.Derived.Erdos257",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences"
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.AffineDivisorAnnihilation"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CanonicalDyadicSectionRank"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CarryDescriptionInformationLoss"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CompositeDilationIdentity"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CoprimeLatticeSumsAndLambert"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DiagonalCertificateTableScales"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DivisorChannelSplitAndSeamDoubling"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DoublingOrbitTransferAndFullDepthPhase"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DyadicPrefixTailBound"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DyadicSectionBasisAndRationalCarry"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExcludedCofactorDensity"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExcludedCofactorEstimate"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExtremalOrderDirectedAndPulse"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyDenominatorFloorExtension"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyExactRangeAndDenominatorExclusion"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyGapDenominatorExclusion"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FirstHarmonicBlockCriteria"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FourLinearConstructionLimits"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GeneralIrrationalityCriteriaAndGapBounds"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GenericCarryRankCeilingCounterexample"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LacunaryFactorialBlockNorm"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertDivisorTransform"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertSigmaRungAndNesterenko"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MersennePrimeSupportAnchors"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MobiusMersenneLadderLogConcavity"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PenultimateStaircaseAndRankCurvature"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.RationalParityCountermodelProperties"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SimultaneousShiftCertificateDepth"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquareBlockBinaryDilationCountermodel"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquaredMersenneDivisorIdentities"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SternBrocotStoppingRecursion"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TailCarryPeriodAndRankFloor"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TemperedOrbitAndSquaredMersenneTail"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ThreeParticularEquivalences"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeChainPaperBand"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicHalfPulseAndAccumulatedResidue"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseBlockAndMobiusInversion"
    },
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseCertificateFailure"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.UnassignedSmoothCount"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.UnassignedSmoothCut"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR21.JointPrimeGapCountermodel"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.AchievementSetTopologyAndFiniteHalf"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleCrtCounts"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleResidueCounts"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleSelection"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleTagFamily"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FeedbackRowStripWitnessAllDepths"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FiniteFamilyCoverCost"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneChannelSurvivalAllHeights"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OddReciprocalDenominators"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OneSidedCertificateHierarchy"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.PostTakeBandLocalisation"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResidueClassSupport"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ScalarLocalisationHeightObstruction"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamEscapeAndTerminalStrip"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamPrefixStabilityLimit"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamQuotientDeficitLimit"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SharedPrefixFamiliesAndMeasureDichotomy"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SkipSafetyAndDivisorZeroRuns"
    },
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquareDepthAndHalfMembershipEquivalences"
    },
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquarefreeSupportEngineCeiling"
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      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TerminalStripExactRowGap"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ThreeBranchRowDynamics"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TotientPeriodCertificateSupply"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungGreedyDecision"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungWitnessHorizon"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.UpperResetBandCertificate"
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    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR21.TwoPrimeSums"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P1041_gamma_uncond"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P1049_a"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P1049_finite_pencil"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P1049_nomahler_uncond"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P243_02"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P243_b"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P243_f"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P243_g"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P249_01"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P249_b"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.P257_03"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperR21Audit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.PaperCompleteR21Audit.Pmisc_01"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.AdelicHeightObstruction"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.AllBaseReciprocalSupportIrrationality"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusCarry"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.BooleanMobiusCofinalExactRows"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityGeometric"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusExactRowCrossing"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusExactRowDoubling"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusExactRowRankTwo"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.BooleanMobiusExactTransition"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusGlobalRepair"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusGreedyReduction"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusLocalRepair"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusSkipRow"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.BooleanMobiusSkipRowCofinal"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.CarrySurvivorExtinction"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.CertificateKernel"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.CofinalStripReturn"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.DiagonalPincerCertificatesT64"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.DyadicPrefixCompression"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.GapFareyBound"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GeometricCoprimality"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCutLocator"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderFatalGapRightTail"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderFinalMiddleCellEscape"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderFiniteShadow"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderFixedTailSocket"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderFullShellSeamBridge"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderHalfMembershipClassification"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderIntegerGreedy"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderLargestSkipInduction"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderProducerLowerBound"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.HalfCylinderSkippedEndpointClassifier"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.HalfCylinderUpperResetBandCertificates"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.HalfDivisorUnitDrop"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.HalfGapMass"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.HalfGreedyFatalGap"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.HalfTrappingReturnCarry"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.HalfUpperResetCriticalBand"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.LcmConeFlatness"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.LcmDiagonalReduction"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.MersenneLambertLadder"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.MobiusSignSupportNoGo"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.PivotAntiReconstruction"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.RationalDenominatorSurvival"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.RationalSupportCarrySkeleton"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.SignedQMomentObstruction"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.SublogDivisorCoverage"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.SuffixCylinderTerminalOnlyBridge"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.TotientActualLcmOrbitSign"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.TotientCarryKernelRigidity"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.TotientMahlerDefect"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.TotientParityCoboundaryCountermodel"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.TotientTailCarryPeriod"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.TotientTailPeriodKiller"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.TropicalCurvatureCarry"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:Erdos249257.TwentyOneQuotientGreedy"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1041.NewtonFlowRaySeparation"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:ErdosProblems.Erdos1041.PaperCriticalValueMeanR10"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:ErdosProblems.Erdos1041.PaperCubicCompletion"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:ErdosProblems.Erdos1041.PaperPrimitiveCompletionR10"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:ErdosProblems.Erdos1041.PaperReflectedCompletion"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:ErdosProblems.Erdos1041.PaperSeparationCounterexample"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperStraightObstructions"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:ErdosProblems.Erdos1041.PaperTrinomial"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "target": "lean-module:ErdosProblems.Erdos1041.PaperTrinomialWholeR21"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperWeightedRefinementsR10"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1041.PrimitiveQuinticInteriorTail"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1041.SharpCollinearChebyshev"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.AdelicHeightBridge"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.AllRow.Producer"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
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    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperLongCapR9"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperNoDecayR9"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperOmegaIndicatorR7"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperR17.SourceConsumers"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperShortCapR9"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.QuantitativeSelectorEscape"
    },
    {
      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos1049.RationalBaseLambert"
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.EightPaperRecoveryAudit",
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      "source": "lean-module:ErdosProblems.Erdos1041.ConnectorR18.PolynomialBranches",
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      "source": "lean-module:ErdosProblems.Erdos1041.ConnectorR18.R13Relevance",
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      "source": "lean-module:ErdosProblems.Erdos249.FiniteDilationJointValue",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.IntegerRadixObservables"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.FiniteDilationLeastResidueRational",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.FiniteDilationJointValue"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.FiniteDilationLinearIndependent",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.FiniteDilationLeastResidueRational"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.FiniteDilationMixedModuli",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.FiniteDilationDyadicClassification"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.FiniteDilationRationalObservables",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.IntegerRadixObservables"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.FiniteEulerSieve",
      "relation": "imports",
      "target": "lean-module:Erdos249257.MersenneLambertLadder"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.FullDepthRayAmplifier",
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      "target": "lean-module:ErdosProblems.Erdos249.PeriodMultipleEscape"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.LcmJumpKillFromDiagonal",
      "relation": "imports",
      "target": "lean-module:Erdos249257.DiagonalPincerCertificatesT31"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.LcmJumpKillFromDiagonal",
      "relation": "imports",
      "target": "lean-module:Erdos249257.LcmConeNonflat"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.CyclotomicRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.CyclotomicProjectionOfShadow"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.CyclotomicRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.PrimePowerJumpDynamics"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.CyclotomicRecoveryAudit",
      "relation": "imports",
      "target": "lean-module:Erdos249257.RepunitMobiusNumerator"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.CyclotomicRecoveryAudit",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.DenominatorBounds",
      "relation": "imports",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.DenominatorRecoveryAudit",
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      "target": "lean-module:Erdos249257.RepunitMobiusNumerator"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.DenominatorRecoveryAudit",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCarryCorrespondence",
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      "target": "lean-module:Erdos249257.CarrySurvivorExtinction"
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCertificateBatch",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCertificateBatch",
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    },
    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCertificateBatch",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteGridCorrespondence",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteGridExample",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FinitePrefixCountermodel",
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      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.GenericTailCertificates"
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FinitePrefixCountermodelEndpoint",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FinitePrefixCountermodelEndpoint",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.GenericTailCertificates",
      "relation": "imports",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.GridArcRealInterface",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.LcmGridCorrespondence",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.MobiusSquareReduction",
      "relation": "imports",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.NumeratorEvaluation",
      "relation": "imports",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.PeriodicIntegerAffine",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.RadicalDecomposition",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.RationalSpacingCorrespondence",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.SignedDyadicClearing",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.SpecifiedTailPeriod",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.TailDepthCorrespondence",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.TailDepthCorrespondence",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmDiagonalConditions",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmDiagonalConditions",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmSeparationAndSign",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmSeparationAndSign",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmShortWindowArithmetic",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.AffineDivisorAnnihilation",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.BinaryDigitChangeDensity",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CanonicalDyadicSectionRank",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CarryDescriptionInformationLoss",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CompositeDilationIdentity",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CompositeDilationIdentity",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CoprimeLatticeSumsAndLambert",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DiagonalCertificateTableScales",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DiagonalCertificateTableScales",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DiagonalCertificateTableScales",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExcludedCofactorEstimate",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyDenominatorFloorExtension",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyExactRangeAndDenominatorExclusion",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FiberMeanOfPrimeNumberTheorem",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.HarmonicGapAndFourTail",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertDivisorTransform",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertSigmaRungAndNesterenko",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertSigmaRungAndNesterenko",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LcmJumpPositionsAndCentralSlack",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LcmJumpPositionsAndCentralSlack",
      "relation": "imports",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MersennePrimeSupportAnchors",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MobiusMersenneLadderLogConcavity",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MobiusMersenneLadderLogConcavity",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NearIntegerIrrationalityCriterion",
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      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NumeratorPolynomialAndMersenneRemainder",
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      "target": "lean-module:Erdos249257.DyadicPrefixCompression"
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NumeratorPolynomialAndMersenneRemainder",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NumeratorPolynomialAndMersenneRemainder",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PenultimateStaircaseAndRankCurvature",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PillaiGcdExpectation",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels",
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    {
      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.RationalParityCountermodelProperties",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SimultaneousShiftCertificateDepth",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SimultaneousShiftCertificateDepth",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquareBlockBinaryDilationCountermodel",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquaredMersenneDivisorIdentities",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TemperedOrbitAndSquaredMersenneTail",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicHalfPulseAndAccumulatedResidue",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseCertificateFailure",
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      "source": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.UnassignedSmoothCount",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.SixMembershipConditions",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusSkipRowCofinal"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.SixMembershipConditions",
      "relation": "imports",
      "target": "lean-module:Erdos249257.CofinalStripReturn"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.SixMembershipConditions",
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      "target": "lean-module:Erdos249257.HalfCutLocator"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.SixMembershipConditions",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.CarryCollapseCorrespondence"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.TerminalSetCorrespondence",
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      "target": "lean-module:Erdos249257.HalfCylinderIntegerGreedy"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.TerminalSetCorrespondence",
      "relation": "imports",
      "target": "lean-module:Erdos249257.TerminalOnlyScaledVanishing"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.AchievementSetTopologyAndFiniteHalf",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.AchievementSetTopologyAndFiniteHalf",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleAssembly",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleAssembly",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleCrtCounts"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleAssembly",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleAssembly",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleTagFamily"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleAssembly",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCoverLowerBoundPaperForm"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleChebyshev",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleCrtCounts",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleEncoding",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleResidueCounts",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleSelection",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleTagFamily",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCoverLowerBound",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.CoverPotentialBounds"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCoverLowerBound",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCoverLowerBoundPaperForm",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCoverLowerBoundPaperForm",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FiniteFamilyCoverCost"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BalancedPulseFanOutCount",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BranchCellHorizonExclusions",
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      "target": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary",
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      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary",
      "relation": "imports",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CompatibleFiniteRowFamily",
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      "target": "lean-module:Erdos249257.BooleanMobiusGlobalRepair"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CriticalDyadicBandCollapse",
      "relation": "imports",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.DyadicBandAndTwoSidedBounds",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.DyadicBandAndTwoSidedBounds",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.EventualNonnegativeMargin",
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      "target": "lean-module:Erdos249257.DyadicPrefixCompression"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.EventualNonnegativeMargin",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.EventualNonnegativeMargin",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FeedbackRowStripWitnessAllDepths",
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      "target": "lean-module:Erdos249257.SuffixCylinderTerminalOnlyBridge"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FeedbackRowStripWitnessAllDepths",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FiniteFamilyCoverCost",
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      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.OptimizedCoverBudget"
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria",
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      "target": "lean-module:Erdos249257.HalfGreedyFatalGap"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyOrbitNoTies",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyOrbitNoTies",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion",
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      "target": "lean-module:Erdos249257.HalfTrappingReturnCarry"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneChannelSurvivalAllHeights",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneChannelSurvivalAllHeights",
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      "target": "lean-module:Erdos249257.RepunitMobiusNumerator"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OddReciprocalDenominators",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OneSidedCertificateHierarchy",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OneSidedCertificateHierarchy",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ScalarLocalisationHeightObstruction",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamEscapeAndTerminalStrip",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamEscapeAndTerminalStrip",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamPrefixStabilityLimit",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SharedPrefixFamiliesAndMeasureDichotomy",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SharedPrefixFamiliesAndMeasureDichotomy",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SkipSafetyAndDivisorZeroRuns",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SkipSafetyAndDivisorZeroRuns",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquareDepthAndHalfMembershipEquivalences",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquarefreeSupportEngineCeiling",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TerminalStripExactRowGap",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TerminalStripExactRowGap",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TerminalStripExactRowGap",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TerminalStripExactRowGap",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ThreeBranchRowDynamics",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ThreeBranchRowDynamics",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TotientPeriodCertificateSupply",
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      "target": "lean-module:Erdos249257.CarrySurvivorExtinction"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungGreedyDecision",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungWitnessHorizon",
      "relation": "imports",
      "target": "lean-module:Erdos249257.DiagonalPincerDecomposition"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungWitnessHorizon",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.UpperResetBandCertificate",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderIntegerGreedy"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.UpperResetBandCertificate",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderUpperResetBandCertificates"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCompleteR7.AnalyticTargets",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR7.Displacement"
    },
    {
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.MersenneSubseriesRigidity"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.ArbitraryWeightMixedClaim"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.PositiveCoverReturn"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.WeightedHereditaryClaim"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAudit",
      "relation": "imports",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.WeightedReturn"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditive",
      "relation": "imports",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditive",
      "relation": "imports",
      "target": "lean-module:Erdos249257.DyadicPrefixCompression"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditive",
      "relation": "imports",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditive",
      "relation": "imports",
      "target": "lean-module:Erdos249257.MersenneLambertLadder"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditive",
      "relation": "imports",
      "target": "lean-module:Erdos249257.MobiusSignSupportNoGo"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditive",
      "relation": "imports",
      "target": "lean-module:Erdos249257.RationalDenominatorSurvival"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave10",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave10",
      "relation": "imports",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave10",
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      "target": "lean-module:Erdos249257.GreedyAchievementSet"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave10",
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    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave10",
      "relation": "imports",
      "target": "lean-module:Erdos249257.HalfCylinderFullShellSeamBridge"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave11",
      "relation": "imports",
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    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave11",
      "relation": "imports",
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    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave11",
      "relation": "imports",
      "target": "lean-module:Erdos249257.BooleanMobiusSkipRowCofinal"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave11",
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    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave12",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave12",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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      "target": "lean-module:Erdos249257.AdelicHeightObstruction"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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    },
    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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      "target": "lean-module:Erdos249257.HalfGapMass"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave2",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave3",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave3",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave4",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave4",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave5",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave6",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave7",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave7",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave7",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave8",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave8",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave8",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave9",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave9",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave9",
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      "source": "lean-module:ErdosProblems.Erdos257.PaperCorrespondenceAuditAdditiveWave9",
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      "target": "lean-module:Erdos249257.AllBaseReciprocalSupportIrrationality"
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    {
      "source": "lean-module:ErdosProblems.Erdos257.SquarefreeSupportIncidence",
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    {
      "source": "lean-module:ErdosProblems.Erdos257.WeightedSupportAveraging",
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      "source": "lean-module:ErdosProblems.Erdos257.WitnessBlockReciprocal",
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      "target": "lean-module:ErdosProblems.Erdos257.WitnessBlockArithmetic"
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      "source": "lean-module:ErdosProblems.Erdos257.WitnessBlockWeighted",
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      "source": "lean-module:ErdosProblems.Erdos257.WitnessBlockWeighted",
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      "source": "lean-module:ErdosProblems.Erdos257.WitnessLogicHost",
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      "source": "lean-module:ErdosProblems.Erdos269.CertificateRangeR11",
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    {
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      "target": "lean-module:ErdosProblems.Shared.IrrationalRotationStaircase"
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    {
      "source": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.LiteralTriangleReal",
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    {
      "source": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.PhaseStripDecomposition",
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      "source": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealBoundDenominatorReduction",
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    {
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    {
      "source": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.UniformRankAudit",
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    {
      "source": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.WeightedShiftArithmetic",
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      "source": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.WeightedShiftValue",
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    {
      "source": "lean-module:ErdosProblems.Erdos269.PaperCompleteR21.TwoPrimeSums",
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    {
      "source": "problem:erdos_251",
      "relation": "explained_by",
      "target": "paper:erdos251-prime-gap-reasoning-surface"
    },
    {
      "source": "problem:erdos_251",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos251.PrimeGapDyadicTail"
    },
    {
      "source": "problem:erdos_257",
      "relation": "explained_by",
      "target": "paper:erdos-257-mersenne-support-subseries"
    },
    {
      "source": "problem:erdos_257",
      "relation": "explained_by",
      "target": "paper:erdos257-expository-sums-never-fractions"
    },
    {
      "source": "problem:erdos_257",
      "relation": "explained_by",
      "target": "paper:erdos257-mersenne-reasoning-surface"
    },
    {
      "source": "problem:erdos_257",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos257.MersenneSubseriesRigidity"
    },
    {
      "source": "problem:erdos_269",
      "relation": "explained_by",
      "target": "paper:erdos-269-three-prime-running-lcm"
    },
    {
      "source": "problem:erdos_269",
      "relation": "explained_by",
      "target": "paper:erdos269-running-lcm-reasoning-surface"
    },
    {
      "source": "problem:erdos_269",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos269.BoundedRadixTailEscape"
    },
    {
      "source": "problem:erdos_269",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos269.CarryLiftExtinction"
    },
    {
      "source": "problem:erdos_269",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos269.ResidueEscape"
    },
    {
      "source": "problem:erdos_269",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos269.RestrictedFloorSum"
    },
    {
      "source": "problem:erdos_269",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos269.ThreeChannelBlockRigidity"
    },
    {
      "source": "problem:erdos_269",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos269.ThreePrimeRunningLcm"
    },
    {
      "source": "problem:erdos_269",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos269.WeightedPhaseCarry"
    },
    {
      "source": "problem:erdos_68",
      "relation": "explained_by",
      "target": "paper:erdos-68-factorial-denominator-irrationality"
    },
    {
      "source": "problem:erdos_68",
      "relation": "explained_by",
      "target": "paper:erdos68-factorial-reasoning-surface"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.CanonicalFactorialDigits"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.ChannelBreakpointRigidity"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.ChannelIntegralCongruence"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.DivisorFactorialCentre"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.EndpointWeightedPrivateSupport"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.FactorialCarry"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.FactorialChannelCertificate"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.FactorialGapPlateauCore"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.FactorialZeroPlateau"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.FiniteDefectAutomaton"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.PrimeUnitTranslator"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.PrimeZeroBranch"
    },
    {
      "source": "problem:erdos_68",
      "relation": "formalized_in",
      "target": "lean-module:ErdosProblems.Erdos68.StrictSuccessorArithmetic"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#lem:two-sheet-bottleneck",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.Counterexample.HausdorffLength"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:ani-degree-seven-counterexample",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.Counterexample.Assembly"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:ani-degree-seven-counterexample",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.Counterexample.HausdorffLength"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:critical-value-separation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.CriticalValueSeparationTransport"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:critical-value-thresholds",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.CriticalValueSeparationTransport"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:critical-value-thresholds",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.SeparationParent"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:scaled-low-critical",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.LowCriticalScaleTransport"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:sextic-spoke",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR20.SexticSpokeWhole"
    },
    {
      "source": "statement:erdos-1041-lemniscate-newton-flow#res:trinomial-all-degree",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperTrinomialWholeR21"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#cor:rational-base-measure",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.RationalBaseThreshold"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#cor:rational-base-measure",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperR17.SourceConsumers"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#prop:weight-factorisation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.RogersFactorisationAnalytic"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#res:rational-base-threshold",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.PrintedContourConstants"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#res:rational-base-threshold",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.RationalBaseThreshold"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#res:sharp-fixed-base",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.SharpFixedBaseShort"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#res:thirtyone-four",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperR17.SourceConsumers"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#res:zudilin-sharp-qorder",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.AllRow.Producer"
    },
    {
      "source": "statement:erdos-1049-rational-base-lambert#thm:geometric-moments",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.GeometricUniversality"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:absorb",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Arithmetic"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:barrier",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:bounded",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:cor",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Arithmetic"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:crt",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:cubicrate",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.SquareSpecialisationUnconditional"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:frontier",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Frontier"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:gcdstab",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Reduction"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:inclusiveone",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.InclusiveOne"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:lcmbounded",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.LcmDefect"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:massscalar",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Frontier"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:originalbounded",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.ProductDefect"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:reduced",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Reduction"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:residue",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.FiniteHorizonResidue"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:step",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Arithmetic"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:step",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:update",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Arithmetic"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:weightedrecord",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.CanonicalRecords"
    },
    {
      "source": "statement:erdos-243-reciprocal-tail-rigidity#res:weights",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.RealCutoffCriterion"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#cor:integral-normal-form",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR8.KernelRelationBasis"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#cor:periodic-freezing",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.PeriodicIntegerAffine"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#lem:bounded-pulse",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.PeriodicAndPulse"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#res:basis",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR8.FullKernelAssemblies"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#res:fulldepth",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.ShortNoteAssemblies"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#res:rankonefloor",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.RankOneSharpFloor"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#res:residueseries",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.RationalObservableClassification"
    },
    {
      "source": "statement:erdos-249-binary-totient-series#thm:kkernelrank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR8.FullKernelAssemblies"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:escape-irrational",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.ExactDenominator"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:escape-irrational",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:gap-nonperiodic",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:infinite",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:infinite",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PrimeGapDyadicTail"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:infinite",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.RealPrimeGapTail"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:irr-equivalence",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:jointcountermodel",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.ArgumentGraph.Results.Erdos251"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:jointcountermodel",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR21.JointPrimeGapCountermodel"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:signedwindow",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.SignedWindow"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:sparserationalisation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.SparseAmbientR9"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:sparserationalisation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.SparsePaperR11"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:true-tail",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.TrueTail"
    },
    {
      "source": "statement:erdos-251-prime-gap-dyadic-series#res:truncation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperTailBoundsR7"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:cylinderhalf",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.SuffixCylinderTerminalOnlyBridge"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:general-repair",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.GeneralRepairCorrespondence"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:mixed-supports",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.ArbitraryWeightMixedClaim"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:mixed-supports",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.WeightedReturn"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:one-over-twenty-one-frontier",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TwentyOneQuotientGreedy"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:period",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:reciprocal-support",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.AllBaseReciprocalSupportIrrationality"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:terminalhalf",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.TerminalSetCorrespondence"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:weighted-cover-incomparability",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.AnalyticSeparationReturn"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:weighted-cover-incomparability",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.ReverseStrengthenedHost"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:weighted-support",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.WeightedHereditaryClaim"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#res:weighted-support",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.WeightedReturn"
    },
    {
      "source": "statement:erdos-257-mersenne-support-subseries#thm:variable-fractional-cover",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.PositiveCoverReturn"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:actual-orbit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7SeriesIdentification"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:admissible-modular-minors",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7ModularMinors"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:cell",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealCutoffs"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:cell",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7BasicAssembly"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:consumer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7BasicAssembly"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:denominator-reduction",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7RationalBridge"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:distinct-height-235",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.DistinctHeightIrrationality"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:dyadic-alphabet",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.DyadicAlphabetWhole"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:exact-onset",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperExactDenominatorR13"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:fibre-prop",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.ThreePrimeRunningLcm"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:finite-cut-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7FiniteCutRank"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:infinite-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7BasicAssembly"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:lcm",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealCutoffs"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:two-prime-transcendence",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR21.TwoPrimeSums"
    },
    {
      "source": "statement:erdos-269-three-prime-running-lcm#res:windowconsumer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7WindowResults"
    },
    {
      "source": "statement:erdos-68-factorial-denominator-irrationality#res:divisor-channel-coordinates",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos68.PaperCompleteDivisorCoordinates"
    },
    {
      "source": "statement:erdos-68-factorial-denominator-irrationality#res:finite-channel-moment-certificate",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos68.PaperCompleteMomentHorizon"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#cor:collinear-erdos-1041",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.CollinearDiameterWhole"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#lem:cubic-safe-root-spoke",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.CubicQuotientFiberCase"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#lem:two-sheet-bottleneck-long",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.Counterexample.HausdorffLength"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#prop:primitive-quintic-two-tail-energy-selector",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PrimitiveQuinticInteriorTail"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#prop:sharp-collinear-chebyshev-comparator",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.SharpCollinearChebyshev"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:ani-degree-seven-counterexample-long",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.Counterexample.Assembly"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:ani-degree-seven-counterexample-long",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.Counterexample.HausdorffLength"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:arity-not-capacity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.ArityNotCapacity"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:circle-slice-packing",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.HyperbolicLawOfCosines"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:complementary-binomial-chords",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.BinomialChords"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:conjecture-p-consumer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.SubcriticalPerimeterPath"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:constant-factor-arity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.ConstantFactorAreaCriteria"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:constant-factor-capacity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.ConstantFactorAreaCriteria"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:constant-factor-path",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.ConstantFactorAreaCriteria"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-proximity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.CriticalTwoRootProximity"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-value-budget",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR20.CriticalMeanWhole"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-value-budget",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCriticalValueMeanR10"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-value-separation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.CriticalValueSeparationTransport"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:critical-value-thresholds",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.CriticalValueSeparationTransport"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:degree-three",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCubicCompletion"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:dual-arity-floor",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.HyperbolicLawOfCosines"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:fp-weighted-all-degree",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperWeightedRefinementsR10"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:locus",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.NewtonFlowRaySeparation"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:low-critical-scale-free",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.LowCriticalScaleTransport"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:one-root-gamma-false",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.LobeUnconditional"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:orlicz-currency",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.MergerScaleOrlicz"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:ray",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR20.NewtonRealTime"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:reflected-critical-value",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperReflectedCompletion"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:scaled-low-critical-path",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.LowCriticalScaleTransport"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:sep-or-false",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperSeparationCounterexample"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:straight-no-go",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperStraightObstructions"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:trinomial-all-degree",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperTrinomial"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:two-nearest-roots",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR20.TwoNearestPolynomial"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#res:value",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR20.NewtonRealTime"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#thm:primitive-quintic-two-tail",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.PrimitiveQuinticClosedDisc"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#thm:primitive-quintic-two-tail",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperPrimitiveCompletionR10"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#thm:sharp-collinear-diameter",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCompleteR21.CollinearDiameterWhole"
    },
    {
      "source": "statement:erdos1041-lemniscate-reasoning-surface#thm:translated-cubic-quotient-fibres",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1041.PaperCubicFibres"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:cor:no-decay-below-square",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperNoDecayR9"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:cor:rational-base-measure",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.RationalBaseThreshold"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:cor:rational-base-measure",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperR17.SourceConsumers"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:prop:rogers-factorisation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.RogersFactorisationAnalytic"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:31over4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.PrintedContourConstants"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:31over4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.PrintedLogConstants"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:31over4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.RationalBaseThreshold"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:allrowinitial",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.AllRowInitialCoefficient"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:archcap",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperLongCapR9"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:archcap",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperShortCapR9"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:boundedfibre",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.AdelicHeightBridge"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:chargeceilings",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:commonmult",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.ZudilinConeArithmetic"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:content",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:corridorbound",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.RationalBaseLambert"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:cyclounit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.ZudilinConeArithmetic"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:endpoints",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:exp",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.RationalBaseLambert"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:finite-pencil",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperR20.FinitePencilProposition"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:forcing",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:jetkernel",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:nocorridor",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.RationalBaseLambert"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:nomahler",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.SimultaneousMahlerSystemUnconditional"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:nomult",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:omega-indicator",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperOmegaIndicatorR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:pade",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:plucker-collapse",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:powerbracket",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:rankfortyone",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:region",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.PrintedContourConstants"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:region",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.RationalBaseThreshold"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:scalar",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:sevenhalves",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.RationalBaseLambert"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:sharpgaps",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperFiniteAssembliesR7"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:sourceheight",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.SourceCoefficientHeights"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:tail-lattice",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.TailPrefixLattice"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:tailrec",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.RationalBaseLambert"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:res:zudilin-sharp-qorder",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.AllRow.Producer"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:thm:geometric-universality",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.GeometricUniversality"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#long1049:thm:sharp-fixed-base",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.PaperCompleteR21.SharpFixedBase"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#res:bottomjet",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.ZudilinConeArithmetic"
    },
    {
      "source": "statement:erdos1049-rational-base-lambert-reasoning-surface#res:boundedfibre",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos1049.QuantitativeSelectorEscape"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:absorb",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:arithmeticrecord",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.ArithmeticWeightedRecord"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:barrier",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ForbiddenBlockCrossing"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:bounded",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:classicalhalfspace",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ClassicalHalfspaceSigns"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:constant",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.NegativeMagnitudeExclusions"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:coprimalitycap",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.WindowAvoidance"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:cor",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:criticalrate",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.AmplifiedRecordEquivalence"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:crt",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ForbiddenBlockCrossing"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:cubicexclusion",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.SquareSpecialisationUnconditional"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:cubicrate",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.SquareSpecialisationUnconditional"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:curvature",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.DynamicCancellation"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:defect",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:descent",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:energycriterion",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.RecordJumpEnergySeries"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:epochenergy",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ProtectedEpochBarrierCount"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:eventual",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:extraction",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.RegularRateExtraction"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:frontier",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Frontier"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gapconstant",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.MaximalGapConstant"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gcdshape",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.CubicProfileGcdShape"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gcdsparse",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Limits"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:gcdstab",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Reduction"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:loglogboundary",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.InclusiveLimsup"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:mass",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Frontier"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:modseven",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.TwoForbiddenWords"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:nonintegralrate",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.NonintegralRegularRate"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:oddpowersupply",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ReducedDenominatorPrimePowers"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:oldmodulussaturation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ReducedStepLocalArithmetic"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:onethreshold",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.InclusiveOne"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:onethreshold",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ProductDefectThresholds"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:periodic",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.NegativeMagnitudeExclusions"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:periodicobstruction",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.DensityTransport"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:powerpersistence",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.PowerPersistence"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:recordamplified",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.AmplifiedRecordEquivalence"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:recorddichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.InclusiveLimsup"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:recorddichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.QuantitativeRecordDichotomy"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:reduced",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Reduction"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:reduciblecase",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.PrimitiveMultiplierSupply"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:residue",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.FiniteHorizonResidue"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:residue",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ForcedOrbitResidueHorizon"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:scale",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Arithmetic"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:scaletwelve",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR20.ScaleTwelve"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:secondorder",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.Arithmetic"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:slownegative",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ExactOrbitRecordDichotomy"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:squarespec",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.SquareSpecialisationDedekind"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:squarespec",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.SquareSpecialisationUnconditional"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:step",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:strausbounded",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.SlowGrowthProductIncrements"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:strausbounded",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.ProductDefect"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:tailratio",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR7.QuantitativeTail"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:transportsquare",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.SquareSpecialisationUnconditional"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:unitrecord",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ReducedDenominatorPrimePowers"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:update",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.ReciprocalTailRigidity"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:valuationtransition",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.ReducedStepLocalArithmetic"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:variablerise",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR21.WindowAvoidance"
    },
    {
      "source": "statement:erdos243-reciprocal-tail-reasoning-surface#long243:res:weightedrecord",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos243.PaperCompleteR11.CanonicalRecords"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a10",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a11",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCertificateBatch"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a12",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCertificateBatch"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailPeriodKiller"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.TailDepthCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailPeriodKiller"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a5",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.TailDepthCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a6",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailPeriodKiller"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a6",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.TailDepthCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a7",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a8",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailPeriodKiller"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:a9",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.SpecifiedTailPeriod"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b10a",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b10b",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b11",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCertificateBatch"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b12",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCarryCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PeriodMultipleAndSecondDifference"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b3",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b4",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmDiagonalReduction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b5",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.LcmGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b6",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.LcmGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b7",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.LcmGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b8",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:b9a",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PeriodMultipleAndSecondDifference"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:c1",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GapFareyBound"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d1",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GeneralIrrationalityCriteriaAndGapBounds"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NearIntegerIrrationalityCriterion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquareBlockBinaryDilationCountermodel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d3",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientMahlerDefect"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR8.FullKernelAssemblies"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientCarryKernelRigidity"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d7",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertDivisorTransform"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d9",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.PrimitiveRationalGapSupply"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:cert:d9",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.RationalSpacingCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a1a",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a1a",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MersenneLambertLadder"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a1b",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.ArithmeticAssemblies"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.QZetaAnchor"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquaredMersenneDivisorIdentities"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a5",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PillaiGcdExpectation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a7",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a7",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquaredMersenneDivisorIdentities"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a8",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a9a",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SternBrocotStoppingRecursion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:a9b",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b1",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.RepunitMobiusNumerator"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.RepunitMobiusNumerator"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.NumeratorEvaluation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b3",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.RadicalDecomposition"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b4",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CyclotomicProjectionOfShadow"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CyclotomicProjectionOfShadow"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.RepunitMobiusNumerator"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b6",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MersenneShadowCyclotomicNoncollapse"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b7a",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.DenominatorBounds"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b7b",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MersenneShadowDenominatorGrowth"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b8a",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.PrimePowerJumpDynamics"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:b8b",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.PrimePowerJumpDynamics"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:d3",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.SignedQMomentObstruction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:d3",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.SignedDyadicClearing"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:e1",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.HarmonicGapAndFourTail"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:e2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.HarmonicGapAndFourTail"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:e3",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.AffineDivisorAnnihilation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#catalogue:mob:f1",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CompositeDilationIdentity"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#cor:b1",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FinitePrefixCountermodelEndpoint"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#cor:digitform",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.BinaryDigitChangeDensity"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#cor:numerator-polynomial-explicit-positive-coefficients",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NumeratorPolynomialAndMersenneRemainder"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:complement-divisibility-after-multiplication",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ScalarLocalisationAndInversePhaseGauge"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:farey",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GapFareyBound"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:gperiod",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.GenericTailCertificates"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:gsound",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.GenericTailCertificates"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:nonvanishing-unique-largest-denominator-exponent",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.SignedQMomentObstruction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:nonvanishing-unique-largest-denominator-exponent",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.SignedDyadicClearing"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:orbit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DoublingOrbitTransferAndFullDepthPhase"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#lem:squared-distance-bound-separated-pairs",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:A10",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:A5-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailPeriodKiller"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:A5-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.TailDepthCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:A9-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.RationalTailPeriodWitnesses"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:AR-03-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmShortWindowArithmetic"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:AR-04-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmShortWindowArithmetic"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:AR-05-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmShortWindowArithmetic"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:AR-06-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmShortWindowArithmetic"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:AR-07",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmDiagonalConditions"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:B10",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:B11-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCertificateBatch"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:B12cons",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteCarryCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:B3",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:B6-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.LcmGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:B7",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:C1-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GeneralIrrationalityCriteriaAndGapBounds"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:C2-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyExactRangeAndDenominatorExclusion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:C2sup",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyGapDenominatorExclusion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:C3-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyExactRangeAndDenominatorExclusion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:CP-01-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TailCarryPeriodAndRankFloor"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:CP-02",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TailCarryPeriodAndRankFloor"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:CP-05-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseBlockAndMobiusInversion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:CP-06",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExtremalOrderDirectedAndPulse"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:CP-07",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExtremalOrderDirectedAndPulse"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D1D2-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D1D2-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GeneralIrrationalityCriteriaAndGapBounds"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D1D2-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquareBlockBinaryDilationCountermodel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D4-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CanonicalDyadicSectionRank"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D5cons",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GenericCarryRankCeilingCounterexample"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D7-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LambertSigmaRungAndNesterenko"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D9-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DyadicPrefixTailBound"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:D9-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.GeneralIrrationalityCriteriaAndGapBounds"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:FR-01",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExtremalOrderDirectedAndPulse"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:FR-02-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PenultimateStaircaseAndRankCurvature"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:MP-01-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseBlockAndMobiusInversion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:NI-01",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmDiagonalConditions"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:SEP-01-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmSeparationAndSign"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:SEP-02-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmSeparationAndSign"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:SEP-03",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmDiagonalConditions"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:SGN-01",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmSeparationAndSign"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:SGN-03",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmSeparationAndSign"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:SK-01-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.RationalTailPeriodWitnesses"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:SK-02",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ActualLcmDiagonalConditions"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:TA-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseBlockAndMobiusInversion"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:TE-02-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PenultimateStaircaseAndRankCurvature"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:TE-03-inv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PenultimateStaircaseAndRankCurvature"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:TE-04",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeStaircaseConditions"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:TE-05",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeStaircaseConditions"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:TE-06",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeStaircaseConditions"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:additional-approximation-hypothesis",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:additional-hypothesis-totient-specific-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DyadicSectionBasisAndRationalCarry"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:b2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ThreeParticularEquivalences"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:b4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicPulseCertificateFailure"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:b5",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CarryDescriptionInformationLoss"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:b6",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FourLinearConstructionLimits"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:b7",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.RationalParityCountermodelProperties"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:badcof",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ExcludedCofactorEstimate"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:bound-preserved-positive-normalised-averaging",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.RankOneSubrankObstruction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:coprime",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:deposits",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CarrySurvivorExtinction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:deposits",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.DiagonalPincerCertificatesT64"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:deposits",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PeriodMultipleEscape"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:deposits",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Skip.LadderT67"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:dickman",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.UnassignedSmoothCount"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:dilations",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.FiniteDilationLinearIndependent"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:dilations",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.FiniteDilationMixedModuli"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:divisor-sum-complement",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DivisorChannelSplitAndSeamDoubling"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:doubling-identity-two-portions-sum",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DivisorChannelSplitAndSeamDoubling"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:exact-rational-approximation-formula",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TemperedOrbitAndSquaredMersenneTail"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:finite-divisor-sum",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:finite-grid-certificate-gives-nonintegral",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FiniteGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:gapwindow",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:gapwindow",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GapFareyBound"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:gcdlayer",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:gcdlayer",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GeometricCoprimality"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:geometric-remainder-bound",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NumeratorPolynomialAndMersenneRemainder"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:geometric-tail-bound",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TemperedOrbitAndSquaredMersenneTail"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:iffs",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.LcmConeFlatness"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:iffs",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.PivotAntiReconstruction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:iffs",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailCarryPeriod"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:iffs",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PeriodMultipleEscape"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:lambertengine",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:mobsq",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.MobiusSquareReduction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:nonzero-minor-survives-inverse-phase",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ScalarLocalisationAndInversePhaseGauge"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:parity",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientParityCoboundaryCountermodel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:period-not-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailCarryPeriod"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:pillai",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GcdMomentCalculus"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:pillai",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PillaiGcdExpectation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:radixresidue",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.IntegerRadixObservables"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:radixresidue",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.RationalIntegerRadixClassification"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:rank",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientCarryKernelRigidity"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:rational-series-preserving-totient-parity",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientParityCoboundaryCountermodel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:route4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DoublingOrbitTransferAndFullDepthPhase"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:separation-larger-than-error-implies",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:shift",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientTailPeriodKiller"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sign",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CarrySurvivorExtinction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sign",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.TotientActualLcmOrbitSign"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:simultaneous-certificates-unrestricted-depth",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SimultaneousShiftCertificateDepth"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:squared-distance-phase-one",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sufficient-accumulated-residue-condition",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicHalfPulseAndAccumulatedResidue"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sufficient-extension",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeCorridorAndSeparation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sufficient-extension-2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ShortWindowSupplyAndSixteenShifts"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sufficient-extension-3",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyDenominatorFloorExtension"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sufficient-inequality",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LcmJumpPositionsAndCentralSlack"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:sum-over-divisor-indices",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DivisorChannelSplitAndSeamDoubling"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:tail-integrality-lcm-grid",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.LcmGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:te-chain",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeChainPaperBand"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:te-chain",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeCorridorAndSeparation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:transfer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DoublingOrbitTransferAndFullDepthPhase"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:two-lattice-sums",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CoprimeLatticeSumsAndLambert"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:uniqueness-under-growth-condition",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TemperedOrbitAndSquaredMersenneTail"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:zetaq",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.QZetaAnchor"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#prop:zetaq",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.SquaredMersenneDivisorIdentities"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#res:fulldepth",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.ShortNoteAssemblies"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#res:rankonefloor",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.RankOneSharpFloor"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:arbitrarily-large-prime-power-lcm",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LcmJumpPositionsAndCentralSlack"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:binary-carry-criterion",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:certificate-four-tail-combination",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:classical-coprime-pair-lambert-identity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CoprimeLatticeSumsAndLambert"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:concatenation-specified-period-multiples",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TotientBlockConcatenation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:coprime-pair-counting-totient",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PhaseEnergyAndForeignResidueProjection"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:denom",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:denom",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GapFareyBound"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:denom-record",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:denomcoprime",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:denominators-mobius-sums",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:denommobsq",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:diagonal-certificate-table",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DiagonalCertificateTableScales"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:doubling-full-totient-difference",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DivisorChannelSplitAndSeamDoubling"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:exact-dyadic-rank-infinite-dimensionality",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DyadicSectionBasisAndRationalCarry"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:first-two-summands-give-positive",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MobiusMersenneLadderLogConcavity"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:fixed-farey-bound",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FareyDenominatorFloorExtension"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:gamma",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FinitePrefixCountermodel"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:gamma",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.FinitePrefixCountermodelEndpoint"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:goodbasegap",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.ArgumentGraph.Results.Erdos249Endpoint"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:hgap-norm",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FirstHarmonicBlockCriteria"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:hgap-real",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FirstHarmonicBlockCriteria"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:hgap-subset",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.FirstHarmonicBlockCriteria"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:lacunary",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.LacunaryFactorialBlockNorm"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:nondivisors-short-lcm-window",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CarrySurvivorExtinction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:nondivisors-short-lcm-window",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR20.LcmGridCorrespondence"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:one-common-certificate-sixteen-shifts",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ShortWindowSupplyAndSixteenShifts"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:one-explicit-witness",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.PrimeJumpWitnessAndMersenneChannels"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:positive-coefficients-numerator-polynomial",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.NumeratorPolynomialAndMersenneRemainder"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:positivity-remaining-residue-inequality",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeCorridorAndSeparation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:prime-satisfying-stated-cyclotomic-conditions",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MersennePrimeSupportAnchors"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:proved-implication",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeCorridorAndSeparation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:proved-implications",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeCorridorAndSeparation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:rationality-carry-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DyadicSectionBasisAndRationalCarry"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:rationality-carry-rank-2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.DyadicSectionBasisAndRationalCarry"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:separation-rational-approximation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TopEdgeCorridorAndSeparation"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:short-window-examples-through-exponent",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.ShortWindowSupplyAndSixteenShifts"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:strict-log-concavity-all-integer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MobiusMersenneLadderLogConcavity"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:sufficient-order-hypothesis-unbounded-prime",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MersennePrimeSupportAnchors"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:two-adic-congruence-that-does",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.TwoAdicHalfPulseAndAccumulatedResidue"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:unbounded-prime-support-mersenne-factors",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MersennePrimeSupportAnchors"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:uniform-positive-gap-rank-one",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.SignedQMomentObstruction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:uniform-positive-gap-rank-one",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR7.ShortNoteAssemblies"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:uniform-positive-gap-rank-one",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.RankOneSubrankObstruction"
    },
    {
      "source": "statement:erdos249-totient-reasoning-surface#thm:values-exponents-one-two",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.MobiusMersenneLadderLogConcavity"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:abel",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PrimeGapDyadicTail"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:affinecollapse",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:block",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:boundedperturbation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:cfexclusion",
      "relation": "stated_in_lean",
      "target": "lean-module:verification.Erdos251LargeCertificate.ErdosProblems.Erdos251.PaperLargeCertificateR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:complete-truncation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.FiniteSeparation"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:denominatorfloor",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperFiniteCertificatesR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:escape-irrational",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:explicit-remainder",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperTailBoundsR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:finite-smallpair",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperFiniteCertificatesR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:freepair",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:gap-nonperiodic",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:infinite",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:irr-equivalence",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:jointcountermodel",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.ArgumentGraph.Results.Erdos251"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:jointcountermodel",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR21.JointPrimeGapCountermodel"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:lcmdiagonal",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.OrderLatticeDiagonal"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:local-targets",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.LocalTargetInterval"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:nonconc-primes",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR21.PerturbedPrimePositions"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:nonconcentration",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperNonconcentrationR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:one-tail-certificate",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.FiniteSeparation"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:parts",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PrimeGapDyadicTail"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:polignacfail",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.LogarithmicCarryAsymptoticsR8"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:polynomialcountermodel",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:shiftedcount",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.ShiftedGapCountingR9"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:signedwindow",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:smallpair",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:smallpair-real",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCoreR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:sparse",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR21.TwoWindowSparsity"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:sparse-nonconcentration",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.SparseNonconcentration"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:sparse-rationalisation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.SparseConstructionAudit"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:sparse-rationalisation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.SparseAmbientR9"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:sparse-rationalisation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.SparsePaperR11"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:telescope",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PrimeGapDyadicTail"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:res:true-tail",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.TrueTail"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:boundedpolignac",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperBoundedCarryR7"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:propagate",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperCompleteR20.RealPropagation"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:totient",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PrimeGapDyadicTail"
    },
    {
      "source": "statement:erdos251-prime-gap-reasoning-surface#long251:xr:truncation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos251.PaperTailBoundsR7"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#cor:257-logarithmic-separation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleAssembly"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#cor:257-logarithmic-separation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCoverLowerBoundPaperForm"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#cor:cd-remaining",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BranchCellHorizonExclusions"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#cor:mersenne-height",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ScalarLocalisationHeightObstruction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#cor:negative-mobius-overshoot",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MobiusSignSupportNoGo"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#cor:tr-half-lcm",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungWitnessHorizon"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:collapse-mech",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:collapse-mech",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:collapse-mech",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:denominator-sandwich",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.DyadicPrefixCompression"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:denominator-survival",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.RationalDenominatorSurvival"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:dyadic-excess-reformulation",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.DyadicPrefixCompression"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:eventually-right-impossible",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFatalGapRightTail"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:fatal-gap-exclusion",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:gap-mass-summability",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:gap-mass-summability",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfGapMass"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:half-divisor-unit-drop",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderIntegerGreedy"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:half-divisor-unit-drop",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfDivisorUnitDrop"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:half-endpoint-kills",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCutLocator"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:largest-false-rank-algebra",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:linear-channel-nogo",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.AdelicHeightObstruction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:linear-channel-nogo",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfTrappingReturnCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:mersenne-tail-weight",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:mixed-prime-power-layer",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MaximalOmegaLayer"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:no-ties",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyOrbitNoTies"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:odometer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ShortWindowDivisorPhase"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:rank-step-trichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:rank-step-trichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCutLocator"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:reverse-carry-word",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:scalar-localization",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ScalarLocalisationHeightObstruction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:seam-upper-or-middle",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderHalfMembershipClassification"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:skipped-endpoint-trichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderSkippedEndpointClassifier"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:sqrt-witness",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.CarryCollapseCorrespondence"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:sqwitness",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.CarryCollapseCorrespondence"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:sqwitness",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquareDepthAndHalfMembershipEquivalences"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:straddle-agrees-greedy",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCutLocator"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:tail-transfer",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:tr-forced-greedy",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungGreedyDecision"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:tr-mod12",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungWitnessHorizon"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#lem:tr-parity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungWitnessHorizon"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:257-finite-witness-rule",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.WitnessLogicIrrational"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:257-logarithmic-initial-interval",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LogarithmicInitialInterval"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:2adic-nogo",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:achievement-set-topology",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.AchievementSetTopologyAndFiniteHalf"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:canon",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:canon",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusGreedyReduction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:canon",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCutLocator"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:carry-survivor-extinction",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TotientPeriodCertificateSupply"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:collapse",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.CofinalCarryCollapse"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:collapsed-list",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.SixMembershipConditions"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:cpgs-equiv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquareDepthAndHalfMembershipEquivalences"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:critical-band-index",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CriticalDyadicBandCollapse"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:exact-lebesgue-measure-dichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SharedPrefixFamiliesAndMeasureDichotomy"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:exponent-gap",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.DenominatorBudget"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:finite-approximations-without-compatibility",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.FeedbackRowStripWitnessAllDepths"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:finite-approximations-without-compatibility",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SharedPrefixFamiliesAndMeasureDichotomy"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:finite-boolSupport-and-onesided",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:finite-state-nogo",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:finite-state-nogo",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BalancedPulseFanOutCount"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:local-void",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:local-void",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos249.PaperCompleteR21.CarryDescriptionInformationLoss"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:local-void",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:mobius-nogo",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MobiusSignAndFiniteCertificates"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:one-orbit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyOrbitNoTies"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:squarefree",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquarefreeSupportEngineCeiling"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:strip-equiv",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SquareDepthAndHalfMembershipEquivalences"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:unsafe-middle-range-exactly-three",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#prop:upper-unconditional",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BranchCellHorizonExclusions"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c1",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCofinalExactRows"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c1",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c10",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c11",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.DyadicBandAndTwoSidedBounds"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c12",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c12",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfUpperResetCriticalBand"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c14",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFullShellSeamBridge"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c15",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamEscapeAndTerminalStrip"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c19",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.EventualNonnegativeMargin"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusSkipRowCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c20",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c3",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CompatibleFiniteRowFamily"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c4",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c4",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c6",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c6a",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c6b",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c7",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusSkipRow"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c8",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusSkipRow"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-c9",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusLocalRepair"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-bridge",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-bridge",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-cross2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusExactRowCrossing"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-mob",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-rank2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusExactRowRankTwo"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i-t7",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i10",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OddReciprocalDenominators"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i11a",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusGreedyReduction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i11b",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusGreedyReduction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i11c",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusGreedyReduction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i12",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityGeometric"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i13",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.DyadicBandAndTwoSidedBounds"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i14",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.UpperResetBandCertificate"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i15",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.UpperResetBandCertificate"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i16",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfTrappingReturnCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i16",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamRowGapAndCarry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i17",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFiniteShadow"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i17",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderIntegerGreedy"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i17",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfDivisorUnitDrop"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i1a",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i1b",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusExactTransition"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i1c",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusSkippedCoreCriticalCapacity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i6",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneQuotientRowRecurrences"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i7",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusExactRowDoubling"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-i9",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusGlobalRepair"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-k-dich",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-k1",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-k2",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-k4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257bm-k9",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257hg-i2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfGapMass"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257hg-i4",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SkipSafetyAndDivisorZeroRuns"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257hg-i5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfGreedyFatalGap"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257hg-i6",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257hg-i6",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFinalMiddleCellEscape"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257hg-i7",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderSkippedEndpointClassifier"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257hg-k12",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.LinearChannelAndMiddleCellExclusion"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-c16",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-c17",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TerminalStripExactRowGap"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-c18",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.BooleanMobiusCriticalCapacityCofinal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-c18",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CofinalStripReturn"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-i2",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.RationalSupportCarrySkeleton"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-i3",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.RationalSupportCarrySkeleton"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-i4a",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SkipSafetyAndDivisorZeroRuns"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-i4b",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.SublogDivisorCoverage"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-i5",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MaximalOmegaLayer"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#record:257rig-k6",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ExactRowDichotomyCountermodels"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:257-logarithmic-counterexample",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ArithmeticCounterexampleAssembly"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:257-mixed-supports",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.ArbitraryWeightMixedClaim"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:257-mixed-supports",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.WeightedReturn"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:257-variable-fractional-cover",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.PositiveCoverReturn"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:257-weighted",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR8.WeightedReturn"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:cd-neg3-impossible",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.BranchCellHorizonExclusions"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:critical-dyadic-band",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfUpperResetCriticalBand"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:dynamics",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ThreeBranchRowDynamics"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:eventually-periodic",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:eventually-periodic-support",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:factorial-twopow-support",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:fatal-absorbing",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:final-middle-cell",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFinalMiddleCellEscape"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:frozen-margin",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFullShellSeamBridge"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:full-support",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:full-support-catalogue",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:geometry",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.AchievementGeometry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:greedy-survival",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.GeneralTargetGap"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:greedy-survival-catalogue",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:greedy-survival-record",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:half-skip-dichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:largest-skip-late",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderHalfMembershipClassification"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:largest-skip-late",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderLargestSkipInduction"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:last-skip-iff-fatal",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFixedTailSocket"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:lcm-gap-engine",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:lower-bound-every-reset",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResetSqrtEscapeHalfMembership"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:master-dichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCutLocator"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:master-identity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.QuotientRowIdentity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:mersenne-channel-growth",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MersenneShadowDenominatorGrowth"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:mersenne-channel-survival",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.MersenneChannelSurvivalAllHeights"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:middle-allright-defect",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:middle-allright-defect",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:middle-allright-defect",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderProducerLowerBound"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:middle-producer-escape",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:mobius-centred-nonneg",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:mobius-centred-nonneg",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderFinalMiddleCellEscape"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:mobius-lambert-identity",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.MersenneLambertLadder"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:multiples-support",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:nine-way-hub",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderHalfMembershipClassification"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:odd-support",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:one-sided",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.OneSidedCertificateHierarchy"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:one-sided-finite-decision-boundary",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.CentredCompletionAndDecisionBoundary"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:pairwise-coprime",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:periodic-support",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.PositivePeriodicSupport"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:perturbed-family-maximality",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderIntegerGreedy"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:purely-periodic-support",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:real-form",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.MersenneConstantDecimal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:real-form",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.QuotientRowReal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:residue-class-support",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.ResidueClassSupport"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:residue-odd",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:seam-limit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.SeamPrefixStabilityLimit"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:second-channel",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:sharp-fatal-gap",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:signed-periodic",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:sqrt-bound-route",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCarryReachability"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:straddle-closed-set",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.GreedyGapCriteria"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:supported-dichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.MersenneSubseriesRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:tempered-orbit-rigidity",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GenericTailOrbitRigidity"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:topology",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.AchievementGeometry"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:topology",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR20.MersenneConstantDecimal"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:tr-finite-decision",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungGreedyDecision"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:tr-witness-exclusion",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.TruncatedRungWitnessHorizon"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:two-channel-cap",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.GreedyAchievementSet"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:two-sided-dyadic",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:two-thirds-band",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.PostTakeBandLocalisation"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:upper-reset-band",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderMiddleCarryLowerBound"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:upper-reset-band",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.HalfCylinderUpperResetBandCertificates"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:upper-reset-band",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos257.PaperCompleteR21.UpperResetBandCertificate"
    },
    {
      "source": "statement:erdos257-mersenne-reasoning-surface#thm:weighted-coeff-engine",
      "relation": "stated_in_lean",
      "target": "lean-module:Erdos249257.CertificateKernel"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:long:denominator-reduction",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealBoundDenominatorReduction"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:long:windowconsumer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.RestrictedFloorSum"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-cancellation",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.LongWindowCapR11"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-dichotomy",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7ActualOrbit"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-escape-endpoint",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.OcticEscapeWhole"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-orbit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7SeriesIdentification"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:actual-tail-bound",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR8RankMajorant"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:all-scale-lattice",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.BoundedLatticeCollision"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:cell",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealCutoffs"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:consumer",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.ResidueEscape"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:count",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7BasicAssembly"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:distinct-height-235",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.DistinctHeightIrrationality"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:drop",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealCutoffs"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:dyadic-alphabet",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7ActualOrbit"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:dyadic-alphabet",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.ThreePrimeRunningLcm"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:exact-denominator",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperExactDenominatorR13"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:fibre",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.ThreePrimeRunningLcm"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:finite-cut-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7FiniteCutRank"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:fixed-base-recoding",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.FixedBaseRecoding"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:infinite-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7BasicAssembly"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:jump-constrained-bound",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.ActualSharpTailMajorantR10"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:lcm",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealCutoffs"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:lead-two-prime",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR21.TwoPrimeSums"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:literal-triangle",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.LiteralTriangleReal"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:no-bounded-length",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7WindowResults"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:pinning",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.EightScaleRigidity"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7BasicAssembly"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:residue-limit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperFixedStartResidueR14"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:short",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealBaseShortInterval"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:strip-decomposition",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.PhaseStripDecomposition"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:tails-equivalence",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7RationalBridge"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:two-prime-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.RealTwoPrimeKernel"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:uniform-rank",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR8UniformRank"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:weighted-shift-identity",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperCompleteR20.WeightedShiftValue"
    },
    {
      "source": "statement:erdos269-running-lcm-reasoning-surface#long269:res:window-growth",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos269.PaperR7WindowResults"
    },
    {
      "source": "statement:erdos68-factorial-reasoning-surface#long68:res:bandbreakpoint",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos68.PaperCompleteSupportedBands"
    },
    {
      "source": "statement:erdos68-factorial-reasoning-surface#long68:res:carry-equivalence",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos68.PaperCompleteExisting"
    },
    {
      "source": "statement:erdos68-factorial-reasoning-surface#long68:res:channel-radius",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos68.PaperCompleteExisting"
    },
    {
      "source": "statement:erdos68-factorial-reasoning-surface#long68:res:companion-orbit",
      "relation": "stated_in_lean",
      "target": "lean-module:ErdosProblems.Erdos68.PaperCompleteExisting"
    },
    {
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      "relation": "publishes",
      "target": "claim:signed_totient_entire_defect_interpolation"
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      "relation": "publishes",
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      "relation": "publishes",
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      "relation": "publishes",
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      "relation": "publishes",
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      "relation": "publishes",
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}