The universe map
1,292 objects and 3,246 connections, generated from the public Lean repository. The first screen shows the 192 navigational objects; load the complete universe to add every Lean module and argument step.
Papers explain, Comparator replays selected exact interfaces, and Palomar may review a prepared unit. None widens Lean's proposition or records peer review or an accepted outcome unless its own source says so.
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- Claims
- Papers
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- Modules
- Argument steps
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Problems (8)
- #68 The factorial-denominator series
- #243 Reciprocal-tail rigidity near the Sylvester recurrence
- #249 The binary totient series
- #251 The prime-gap dyadic series
- #257 Reciprocal sums over infinite exponent supports
- #269 Three-prime running least common multiples
- #1041 Short connections inside polynomial lemniscates
- #1049 Lambert-type series at rational bases
Papers (13)
- Factorial Carries and Finite Channel Obstructions
- Excluding the Bounded Negative Part
- A Basis for the 2-Kernel of Euler's Totient
- The Binary Totient Series
- An Integral-Shift Criterion for Dyadic Tail Recurrences
- Denominator Periods, Rational-Value Constraints and Achievement-Set Geometry
- Reciprocal Mersenne Subseries
- The Three-Prime Running Least Common Multiple
- Newton Flow and Critical-Value Ray Separation
- Arithmetic Boundaries at Base 3/2
- From Lean Proofs to Public Claims
- From a Cold Clone to a Proof Receipt
- Plectis: What a Stranger Can Check
Repository documents (14)
Checked claims (103)
- Finite foreign-residue projection reduction
- Scalar-localisation height obstruction
- Adjacent-pair phase separation reduction
- Affine residue state and old-channel annihilation
- All-base totient-kernel reduction, spanning, and conditional rank
- Boolean–Möbius carry certificate equivalence
- Boundary-pulse normalization at the largest-skip crossing
- Campbell shift-synchronization strategy boundary
- Canonical strict-jump slack reduction
- Certificate completeness
- Exact reduction of #249 to finite decidable certificates
- Initial certified-kill segment and generated certificates
- Cofinal square-root-strip return closure
- Composite dilation defect identity
- Concrete adjacent-cut producer-carry coordinates
- Concrete finite seam adapter
- Unconditional denominator exclusion for the totient constant
- Fresh-loss projection and suffix-supply reduction
- Exact full-target reduction on the lcm diagonal
- T64 diagonal-pincer endpoint certificate
- T64 diagonal-pincer primality closure
- Dyadic-prefix, block-safety, and primitive-overshoot interfaces
- Explicit basis of the dyadic totient kernel span
- Dyadic totient-kernel finite-level rank
- The Erdős–Borwein constant E is irrational
- Full-support Erdős–Borwein irrationality, every integer base b ≥ 2
- Erdős #249: irrationality of S = ∑ φ(n)/2ⁿ
- Fatal-gap and eventual-right seam classification
- Upper and first middle producers cannot feed an all-right tail
- Rank-26 phase sieve for the final middle -2 cell
- First-harmonic gap implies a finite certificate
- Complex first-harmonic pivot decomposition
- Fixed-coefficient rewind contraction
- Fixed-precision valuation-unit no-go theorem
- Fixed-tail survival equivalence at every actual skip
- Affine three-scale frontier for the flexible odd window
- Flexible three-rank odd-window reduction
- Fresh-prime endpoint-deficit decomposition
- Greedy geometry of the Mersenne achievement set
- Half-carry reachability and compactness
- Finite shadows of the half cylinder
- Half-divisor unit coefficient drop at the feedback row
- Exact band localization of the final skip between two takes
- Positive half-membership classification in seam coordinates
- Exact rational second-channel reduction for the target one half
- Half-trapping reverse-carry interface
- Integer-greedy first-wrap reduction
- Largest skipped-rank gap and successor propagation
- Largest-skip induction from a quantified first-crossing hypothesis
- Last-producer tail-escape reduction
- LCM factor-ideal anchor-pulse no-go theorem
- Localized protected seam compactness
- The Mersenne–Lambert ladder identities
- Exact Mersenne-shadow denominator and survivor bounds
- Finite Mersenne tail-atom determinant boundary
- Finite-prefix middle-producer cardinality reduction
- Mixed cofinal half-carry fan-in
- Mixed prime-power support-layer identity
- Möbius-sign support one-half no-go
- Conditional orthogonal-petal sunflower reduction
- Parity obstruction for the reduced margin socket
- Period-four signed residue-selection obstruction
- Eventually-periodic nonnegative weighted Lambert irrationality
- Periodic signed-weight irrational-or-terminating dichotomy
- Pivot anti-reconstruction and window-pair reduction
- Exact power-of-two one-bit lift
- Irrationality of the prime-support series ∑_p 1/(2^p − 1)
- Primitive Euler-coordinate finite-jet obstruction
- Prime-power reduced-denominator unit-gap ceiling
- Exact producer-carry residual and sign criteria
- Exact quarter-band failure cells for adjacent seam cuts
- Realized rewind phase identity
- Rationality-forced reciprocal-mass lower bound
- Exact right-branch window and reset-deficit escape law
- Residual-gauge obstruction for monomial minors
- Finite rewind boundary-pair obstruction
- Operational bridge from rewind seams to protected next-row seams
- Exact seam-hole to producer-carry alignment identity
- Selected half-carry windows
- Conditional suffix-cylinder feedback and child-gap recurrence
- Verified finite suffix-cylinder stages through depth 52
- Computed depth-18 selected half-carry window base
- Transcendence of ∑ σ(m)/2^m
- Signed dyadic-moment algebra
- Square-CRT correction suppression
- Squared-Lambert identities for divisor count and the first gcd moment
- Sharp squared-Mersenne diagonal enclosure
- Irrationality of the base-2 squarefree-support series
- Reduced-direction normalization and Stern–Brocot cylinder law
- Fibonacci and continuant stability of Stern–Brocot runs
- Sublogarithmic divisor-coverage zero windows
- Named infinite-support irrationality families toward #257
- Tempered tail-orbit rigidity criterion
- Terminal-only cofinal square-root-strip closure
- Scaled terminal-vanishing closure
- Unconditional carry-kernel anti-compression
- Fair-coin coprimality form of the totient constant
- Verified transport-window certificates
- Transport and curvature reductions for Erdős #249
- Canonical quotient-greedy and scaled-remainder frontier at 1/21
- Carry states are unbounded over infinite rational-valued supports
- Erdős #257, universal form
- Upper-reset dyadic-band certificates through row 30
Comparator review families (50)
- A bounded search records finite geometric evidence. not_applicable_not_a_lean_theorem
- The Newton value equation and its exponential first integral are checked exactly. not_selected_compact_calculus_family
- The paper identifies an invalid local saddle block in a claimed unrestricted proof. not_applicable_not_a_lean_proposition
- Distinct positive rays exclude a finite Newton connection. represented_by_translation_avoidance_targets
- A quantified small constant perturbation keeps every polynomial root inside the open unit disc. targeted
- Collision translations are parameterised by real affine lines and an arbitrarily small common translation avoids finitely many of them. targeted
- The coordinatewise corridor forces a power-versus-linear inequality and cannot occur at base 3/2. targeted
- Endpoint residues at 2 and 3 exclude a common multiplier under unit-endpoint hypotheses. represented_by_selected_coordinatewise_no_go
- Binary selectors collide in the four-jet signature at the stated rank and depth. not_selected_finite_combinatorial_family
- Exact height-region inclusions and exclusions, Padé denominator-exponent bounds, and a rectangular Hermite-Padé threshold no-go are checked. not_selected_multiple_scoped_arithmetic_families
- The exact rational-base cleared-tail recurrence exposes exponential denominator-base forcing absent at integer bases. targeted
- Integer scalar content changes analytic error and exterior determinant by matching factors, yielding no margin by itself. represented_by_selected_coordinatewise_no_go
- Irrationality at 7/2 is obtained from an external analytic criterion whose elementary height hypothesis is checked in Lean. not_applicable_to_external_irrationality_conclusion
- Normalised vanishing excludes a cofinally bounded negative part and forces eventual Sylvester behaviour. targeted
- A bounded-rise sequence cannot remain coprime to fresh pairwise-coprime moduli; reduced tails inherit this obstruction. represented_by_stronger_selected_boundary_theorem
- Exact update and defect identities, scale equivariance, zero absorption, and eventual recovery of the Sylvester recurrence. represented_by_selected_boundary_theorems
- Finite normalised negative mass forces eventual zero and hence the Sylvester recurrence. not_selected_deep_state_vocabulary
- Constant, eventually constant, periodic, and eventually periodic negative-error orbits are excluded in their stated regimes. targeted_representative_periodic_theorem
- Eventually periodic nonnegative rational weights give an irrational Lambert series. not_selected_prior_result
- Rationality forces a tempered integral tail orbit with unbounded finite-level carry rank. not_selected_deep_orbit_vocabulary
- Pointwise, cofinal, lcm-diagonal, and separated-window certificate supplies are exact or sufficient reformulations. not_selected_deep_certificate_vocabulary
- A Farey denominator exclusion through 7.96e34, sharp for its selected window, and diagonal certificates through t=82. not_selected_finite_family_has_separate_receipt
- For every base k at least 2, Lean checks the arithmetic reduction, exact nonmultiple-residue coordinates, unconditional canonical spanning, and exact rank k^e+1 conditional on canonical-family linear independence. not_selected_external_independence_boundary
- An explicit odd-core basis and relation normal form for the full dyadic totient kernel. targeted
- An independent constructive proof of exact finite-level dyadic rank 2^e+1, together with a kernel-checked full-kernel infinite-dimensionality corollary already implied by Coons's non-2-regularity theorem. targeted
- The totient series is rewritten as a Lambert series with explicit nonnegative, unbounded prime-power coefficients. represented_by_basis_and_rank_targets
- Prime gaps are unbounded and non-eventually-periodic, while an explicit nonperiodic unbounded countermodel still has rational sum. targeted_unboundedness_theorem_only
- Block identities and exact denominator criteria classify rationality through integral positive tail shifts. not_selected_abstract_family_represented_in_manifest
- Exact finite summation by parts, the unconditional infinite prime-gap identity, and irrationality equivalence. targeted
- Cofinal adjacent small mismatches would rule out eventual integral shifts for the prime-gap tail. not_selected_open_producer_hypothesis
- Odd rational denominators give totient-length integral shifts, and integrality propagates through the recurrence. represented_by_integral_shift_family
- Compactness, perfectness, total disconnectedness, nowhere density, and measure one for the unrestricted achievement set. targeted_measure_theorem
- The multiplicative order of the base modulo a reduced finite-sum denominator is the support lcm, forcing denominator growth. targeted
- Exact greedy characterisations and finite-support exclusions isolate the remaining 1/2 and 1/21 alternatives. not_selected_deep_greedy_state_vocabulary
- Full, factorial, power-of-two, multiple, pairwise-coprime, eventually periodic, residue-class, and odd supports are formalised. targeted_full_support_representative
- Rational infinite supports force unbounded scaled tails, sublogarithmic zero windows, and reciprocal-mass constraints. not_selected_deep_support_vocabulary
- Support-restricted coding is injective and the associated achievement set has exact finite-complement measure or zero for infinite complement. targeted_measure_dichotomy
- Lean checks squarefree incidence and no-go statements; the irrationality conclusion uses an external analytic theorem in the paper. not_applicable_to_external_irrationality_input
- Cofinal local-window residue escape would rule out bounded positive carries after an unproved rationality-to-carry bridge. not_selected_unproved_bridge_and_deep_predicates
- The exact dyadic block alphabet is 2, 6, 10, and 30. represented_by_three_prime_structure_target
- Finite height-fibre normal form and a quadratic smooth-shell multiplicity bound. represented_by_three_prime_structure_target
- The 2,3,5 kernel is not rank one and its smallest displayed minor equals -1/15. targeted
- A local-window checker searches 106666 denominator and start pairs and records small certificates. not_applicable_not_a_lean_theorem
- Exact running-LCM product, logarithmic-cell constancy, coordinate jump ratios, and jump count. targeted_running_lcm_identity
- Both two-prime running-lcm series are proved transcendental by an authored deduction from an external theorem. not_applicable_not_a_lean_declaration
- Exact equivalence between irrationality, cofinally many non-unit carries, and cofinal strict-successor divisibility failures. targeted
- Finite channel congruences, a two-term prime-channel corrector, and endpoint-weighted projection rigidity. represented_by_isolated_headline
- Cofinal zero-branch or large private-factor hypotheses imply the required irrationality conclusion. not_selected_deep_project_predicate_stack
- Lean checks small exact misses; a hash-bound GMP scan reaches index 300000 and yields the corresponding finite denominator exclusion. not_applicable_to_external_execution
- A paper deduction gives a lower bound for the lcm of factorial-gap denominators using an external multiplicity theorem. not_applicable_not_a_lean_declaration
Lean modules (1,021)
The 40 modules with per-problem declaration counts are listed here; the complete set is in the loaded universe and in the repository.
ErdosProblems.Erdos1041.NewtonFlowRaySeparationErdosProblems.Erdos1049.HermitePadeNoGoErdosProblems.Erdos1049.QAperyDiagonalNonEquivalenceErdosProblems.Erdos1049.RationalBaseLambertErdosProblems.Erdos1049.RationalPadeArithmeticErdosProblems.Erdos1049.ZudilinConeArithmeticErdosProblems.Erdos1049.ZudilinHeightRegionErdosProblems.Erdos243.DynamicCancellationErdosProblems.Erdos243.FeedbackRealizabilityErdosProblems.Erdos243.FiniteHorizonResidueErdosProblems.Erdos243.GlobalLcmHeightErdosProblems.Erdos243.LcmCriticalBoundaryErdosProblems.Erdos243.PrimitivePrefixRigidityErdosProblems.Erdos243.ReciprocalTailRigidityErdosProblems.Erdos243.SparseResetRecoveryErdosProblems.Erdos243.WeightedCRTRepairErdosProblems.Erdos249.FiniteEulerSieveErdosProblems.Erdos249.PrimeRayCyclotomicCurvatureErdosProblems.Erdos249.TotientStrictPrimeEscapeErdosProblems.Erdos251.PrimeGapDyadicTailErdosProblems.Erdos257.MersenneSubseriesRigidityErdosProblems.Erdos269.BoundedRadixTailEscapeErdosProblems.Erdos269.CarryLiftExtinctionErdosProblems.Erdos269.ResidueEscapeErdosProblems.Erdos269.RestrictedFloorSumErdosProblems.Erdos269.ThreeChannelBlockRigidityErdosProblems.Erdos269.ThreePrimeRunningLcmErdosProblems.Erdos269.WeightedPhaseCarryErdosProblems.Erdos68.CanonicalFactorialDigitsErdosProblems.Erdos68.ChannelBreakpointRigidityErdosProblems.Erdos68.ChannelIntegralCongruenceErdosProblems.Erdos68.DivisorFactorialCentreErdosProblems.Erdos68.EndpointWeightedPrivateSupportErdosProblems.Erdos68.FactorialCarryErdosProblems.Erdos68.FactorialChannelCertificateErdosProblems.Erdos68.FactorialZeroPlateauErdosProblems.Erdos68.FiniteDefectAutomatonErdosProblems.Erdos68.PrimeUnitTranslatorErdosProblems.Erdos68.PrimeZeroBranchErdosProblems.Erdos68.StrictSuccessorArithmetic
Argument steps (79)
Steps of the recorded argument graph, published in graph.json with their relations.