Families
OpenAI groups related papers into 372 families. Each row links to the papers, their Lean statements and independent assessments.
The papers cited most within the release are listed on their own page.
No family has an explanation written for the atlas yet. An explanation for mathematicians outside a family’s area is one of the most useful things to add, and each family page has a button to offer one. The contributing guide sets out what to include and how the work is reviewed. Read CONTRIBUTING.md
Every family
372 of 372 families shown
MathVet and cert-machine assessed whether each family’s Lean statements express the whole result OpenAI describes in its catalogue. Each column gives Atlas’s description first, followed by the group’s own term in quotation marks. Menu counts are for the whole release.
No family matches these filters.
| Family | Lean statements | MathVet | cert-machine | Proofs reported accepted | Other proof or calculation reports | Explanation | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 001 | Milne’s rationality conjecture and algebraic specializationNumber theoryOne earlier edition | Number theory | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 002 | The full BSD formula from low Selmer corankNumber theoryThree earlier editions | Number theory | 3 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | Two explanations by others |
| 003 | The quasi-Riemann hypothesisNumber theory | Number theory | 3 | 4 | 4 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 4 of 4 | None recorded | Nine explanations by others |
| 004 | Hilbert’s tenth problem over ℚNumber theoryTwo earlier editions | Number theory | 2 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 005 | Irrationality of Catalan’s constantNumber theory | Number theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Exact calculations for finite claims | One problem reported, not judged by the atlas |
| 006 | Goldfeld’s conjecture: densities and mean analytic rankNumber theoryTwo earlier editions | Number theory | 2 | No Lean statement | 5 | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by othersOne problem reported, not judged by the atlas |
| 007 | Ordinary two-point correlations and the corrected Elliott conjectureNumber theory | Number theory | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 008 | The Deligne–Drinfeld conjectureNumber theory | Number theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 009 | Function-field reconstruction from Milnor K-theory and Galois dataNumber theory | Number theory | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 010 | Unrestricted pro-modularity at the prime twoNumber theoryTwo earlier editions | Number theory | 3 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 011 | Prime-factor statistics of \(p-1\)Number theory | Number theory | 3 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 012 | Independent largest prime factors of consecutive integersNumber theory | Number theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 013 | Ostmann’s inverse Goldbach conjectureNumber theory | Number theory | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 014 | Restricted geometric Langlands, global Arthur enhancements, and generic RamanujanNumber theory | Number theory | 8 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 015 | Torus-packet equidistribution in prime, quartic, and sextic degreesNumber theory | Number theory | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 016 | Zilber–Pink in abelian varieties and the Siegel threefoldNumber theory | Number theory | 4 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 017 | The irrationality exponent of π is 2Number theoryThe two readers disagree | Number theory | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | Proofs of selected steps in HOL Light | Two explanations by others |
| 018 | The Margulis–Platonov conjecture over global fieldsNumber theory | Number theory | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 019 | The local p-adic section conjecture and global consequencesNumber theoryOne earlier edition | Number theory | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 020 | Squarefree quartics and power-free polynomial valuesNumber theory | Number theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 021 | A quadratic bound for Jacobsthal’s functionNumber theory | Number theory | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | One explanation by others |
| 022 | The weak inhomogeneous Duffin–Schaeffer conjectureNumber theory | Number theory | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 023 | Patterson’s first moment for cubic Gauss sumsNumber theory | Number theory | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 024 | An asymptotic formula for the number of totientsNumber theory | Number theory | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 025 | Short Egyptian fractionsNumber theory | Number theory | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | One explanation by others |
| 026 | Positive lower density of large prime gapsNumber theory | Number theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 027 | Potential integral density on curve character varietiesNumber theory | Number theory | 1 | 1 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “SUPPORT-ONLY” | 1 of 1 | None recorded | No explanation yet |
| 028 | Uniformly bounded components of Gaussian-prime graphsNumber theory | Number theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Proofs of selected steps in HOL Light | No explanation yet |
| 029 | Primitive roots for every admissible integer baseNumber theory | Number theory | 2 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 030 | Modularity of elliptic curves over imaginary quadratic fieldsNumber theory | Number theory | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | Two explanations by others |
| 031 | Uchida’s conjecture for open homomorphisms of Galois groupsNumber theory | Number theory | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 032 | The rational Hodge conjecture for CM abelian varietiesAlgebraic and complex geometryThree earlier editions, three withdrawn | Algebraic and complex geometry | 5 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by othersNine problems reported, not judged by the atlas |
| 033 | Iitaka subadditivity, variation, and logarithmic additivityAlgebraic and complex geometry | Algebraic and complex geometry | 5 | 1 | 5 | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | No explanation yet |
| 034 | Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivityAlgebraic and complex geometryTwo earlier editions | Algebraic and complex geometry | 14 | No Lean statement | 8 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 035 | Log-canonical threefold abundance in numerical dimension oneAlgebraic and complex geometry | Algebraic and complex geometry | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 036 | Numerical semiampleness and generalized minimal modelsAlgebraic and complex geometryOne earlier edition | Algebraic and complex geometry | 4 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 037 | The ordinary-double-point volume gapAlgebraic and complex geometry | Algebraic and complex geometry | 2 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 038 | Fujita’s freeness conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 039 | Nagata’s conjecture and maximal Seshadri constantsAlgebraic and complex geometry | Algebraic and complex geometry | 4 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | No explanation yet |
| 040 | Bloch’s conjecture for complex surfacesAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 041 | Hyperkähler SYZ and projective-space basesAlgebraic and complex geometry | Algebraic and complex geometry | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 042 | Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VIIAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 043 | P = W for fixed-determinant SLn moduli spacesAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 044 | The equivariant cohomological Hikita conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 046 | Shafarevich counterexamples in dimension two and with large fundamental groupAlgebraic and complex geometry | Algebraic and complex geometry | 2 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 047 | Zariski cancellation and affine fibrations over the complex numbersAlgebraic and complex geometry | Algebraic and complex geometry | 1 | 1 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 048 | A characteristic-zero counterexample to Lipman–ZariskiAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 049 | A stable-coordinate counterexample in four variablesAlgebraic and complex geometry | Algebraic and complex geometry | 2 | 3 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | Proofs of selected steps in HOL Light, exact calculations for finite claims | No explanation yet |
| 050 | A counterexample to Griffiths’ positivity conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 051 | Kobayashi’s canonical-ampleness conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 052 | Tangent splittings and product decompositionsAlgebraic and complex geometryThe two readers disagree | Algebraic and complex geometry | 2 | 2 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | None recorded | No explanation yet |
| 053 | A counterexample to Pixton completeness in ChowAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 054 | Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associationsAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 055 | Gepner symmetry and large-volume stability on threefoldsAlgebraic and complex geometry | Algebraic and complex geometry | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 056 | Termination of projective and Kähler fourfold minimal model programsAlgebraic and complex geometryThree earlier editions | Algebraic and complex geometry | 5 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 057 | Fundamental groups of special complex varieties and root orbifoldsAlgebraic and complex geometry | Algebraic and complex geometry | 3 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 058 | Semialgebraic universal covers and bounded domainsAlgebraic and complex geometry | Algebraic and complex geometry | 2 | 1 | 2 | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | No explanation yet |
| 059 | Counterexamples to Zariski’s multiplicity conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | No explanation yet |
| 060 | The Global Spherical Shell conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 062 | Projective contact classification and the LeBrun–Salamon conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 063 | The generalized Mukai conjectureAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 064 | Topological triviality of μ-constant surface singularitiesAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 065 | Virasoro constraints for complete intersections and projective-bundle towersAlgebraic and complex geometry | Algebraic and complex geometry | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 066 | Bounded klt complements for Fano contractionsAlgebraic and complex geometry | Algebraic and complex geometry | 2 | 1 | 1 | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “SUPPORT-ONLY” | 1 of 1 | None recorded | No explanation yet |
| 067 | The Campana–Peternell conjecture in dimension sixAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | No explanation yet |
| 068 | Anticanonical nonvanishing in every dimensionAlgebraic and complex geometry | Algebraic and complex geometry | 7 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 069 | Global quantum geometric Langlands at irrational levelAlgebraic and complex geometry | Algebraic and complex geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 071 | Koebe’s circle-domain conjectureReal and complex analysis | Real and complex analysis | 2 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 072 | Brennan’s conjecture and the integral-means spectrumReal and complex analysisThe two readers disagree | Real and complex analysis | 2 | 3 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 3 of 3 | None recorded | No explanation yet |
| 073 | The Falconer distance conjectureReal and complex analysis | Real and complex analysis | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 074 | Kakeya in three and four dimensionsReal and complex analysis | Real and complex analysis | 2 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | Two explanations by others |
| 075 | The \(L\log L\) Fourier-convergence conjectureReal and complex analysis | Real and complex analysis | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 076 | Real ultraflat Littlewood polynomials and unbounded binary merit factorsReal and complex analysis | Real and complex analysis | 3 | 2 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | No explanation yet |
| 077 | Fourier restriction for positively curved surfacesReal and complex analysis | Real and complex analysis | 2 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 078 | The three-dimensional Bochner–Riesz conjectureReal and complex analysis | Real and complex analysis | 1 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 079 | Local smoothing in three dimensionsReal and complex analysis | Real and complex analysis | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 080 | The exact Sobolev endpoint for Schrödinger convergenceReal and complex analysis | Real and complex analysis | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 081 | Riesz transforms and rectifiability in higher codimensionReal and complex analysis | Real and complex analysis | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 082 | Annular variation and dyadic absolute bounds for the triangular Hilbert transformReal and complex analysis | Real and complex analysis | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 083 | Hilbert transforms along Lipschitz directionsReal and complex analysis | Real and complex analysis | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 084 | The geometric case of the Erdős similarity conjectureReal and complex analysis | Real and complex analysis | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 085 | Endpoint Sobolev regularity of centered disk averagesReal and complex analysis | Real and complex analysis | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 086 | An L3 bound for the trilinear Hilbert transformReal and complex analysis | Real and complex analysis | 1 | No Lean statement | 3 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 087 | The Mahler conjectures, functional inequalities and polar-product symplectic widthConvex and metric geometryThe two readers disagree | Convex and metric geometry | 3 | 4 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 4 of 4 | Exact calculations for finite claims | Five explanations by others |
| 088 | Sharp projection-body inequalities and a counterexample to simplex maximizationConvex and metric geometry | Convex and metric geometry | 2 | 3 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 3 of 3 | Exact calculations for finite claims | No explanation yet |
| 089 | Bounded-distortion L1 embeddings of planar and bounded-treewidth graphsConvex and metric geometryThe two readers disagree | Convex and metric geometry | 2 | 2 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 2 of 2 | None recorded | No explanation yet |
| 090 | Triangular-lattice optimality, long-range Riesz and Coulomb energies, and spherical logarithmic energyConvex and metric geometry | Convex and metric geometry | 4 | 4 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 3 of 4 | Exact calculations for finite claims | No explanation yet |
| 091 | Logarithmic and Lp Brunn–Minkowski inequalities and the B-conjectureConvex and metric geometry | Convex and metric geometry | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 092 | The optimal order of convex-body covering densityConvex and metric geometry | Convex and metric geometry | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 093 | Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measuresConvex and metric geometry | Convex and metric geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 094 | Subpolynomial dimension reduction in LpConvex and metric geometryThe two readers disagree | Convex and metric geometry | 1 | 1 | 1 | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 095 | Hyperbolicity cones without semidefinite liftsConvex and metric geometry | Convex and metric geometry | 3 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 096 | The Gaussian propeller conjecture in every dimensionConvex and metric geometryThe two readers disagree | Convex and metric geometry | 1 | 1 | 1 | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 097 | The Euclidean Steinitz–Bergström boundConvex and metric geometryThe two readers disagree | Convex and metric geometry | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 098 | Compact counterexamples to bi-Lipschitz dimension reductionConvex and metric geometry | Convex and metric geometry | 1 | 2 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 099 | The sharp exponential scale of edit-distance distortionConvex and metric geometry | Convex and metric geometry | 3 | 4 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 4 of 4 | None recorded | No explanation yet |
| 100 | Cylinder coverings below the half-area boundConvex and metric geometry | Convex and metric geometry | 4 | 3 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | Exact calculations for finite claims | No explanation yet |
| 101 | The sharp simplex conjecture for isotropic constantsConvex and metric geometry | Convex and metric geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | No explanation yet |
| 102 | The Unique Games Conjecture and optimal approximation thresholdsTheoretical computer science | Theoretical computer science | 5 | 5 | 2 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 5 | None recorded | Four explanations by others |
| 103 | Exact derandomization of logarithmic space: \(\mathsf L=\mathsf{RL}=\mathsf{BPL}\)Theoretical computer scienceThe two readers disagree | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | One problem reported, not judged by the atlas |
| 104 | Quasipolynomial algorithms for mean-payoff, stochastic and parity gamesTheoretical computer science | Theoretical computer science | 4 | 2 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNDECLARED” | 2 of 2 | Exact calculations for finite claims | No explanation yet |
| 105 | Perfect completeness for 2-to-1 gamesTheoretical computer science | Theoretical computer science | 1 | 1 | 2 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 106 | Hardness of coloring three-colorable graphsTheoretical computer science | Theoretical computer science | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 107 | Matrix multiplication with exponent at most 9/4Theoretical computer scienceThe two readers disagree | Theoretical computer science | 3 | 2 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 2 of 2 | Exact calculations for finite claims | Two explanations by othersOne problem reported, not judged by the atlas |
| 108 | A cubic permanent–determinant lower boundTheoretical computer science | Theoretical computer science | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 109 | Integer multiplication below \(n\log n\)Theoretical computer science | Theoretical computer science | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 110 | Optimal-order randomized k-server on arbitrary metricsTheoretical computer science | Theoretical computer science | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | One problem reported, not judged by the atlas |
| 111 | One-sample matroid prophet inequalities against an almighty adversaryTheoretical computer science | Theoretical computer science | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 112 | Beyond the square-root exponent for depth-three circuitsTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 113 | Approximate counting and entropy of perfect matchingsTheoretical computer science | Theoretical computer science | 2 | 6 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 6 of 6 | None recorded | No explanation yet |
| 114 | Approximate counting of common integer polymatroid basesTheoretical computer science | Theoretical computer science | 2 | 1 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 115 | Sampling and counting contingency tables with arbitrary marginsTheoretical computer science | Theoretical computer science | 2 | 1 | 2 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 116 | Uniform black-box noncommutative identity testing across characteristicsTheoretical computer science | Theoretical computer science | 3 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | No explanation yet |
| 117 | Uniform sparsest cut: hardness and semidefinite gapsTheoretical computer science | Theoretical computer science | 2 | 1 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 118 | Bin packing and unbounded configuration-LP gapsTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 119 | The Courtade–Kumar and Hellinger conjecturesTheoretical computer science | Theoretical computer science | 2 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | Exact calculations for finite claims | No explanation yet |
| 120 | Almost-linear-time exact matching and prescribed-degree factors in general graphsTheoretical computer science | Theoretical computer science | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 121 | Almost-linear approximation of edit distanceTheoretical computer science | Theoretical computer science | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 122 | Quantitative trace-reconstruction bounds with a uniform decoderTheoretical computer science | Theoretical computer science | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | One explanation by others |
| 124 | Polynomial-time scheduling on three identical machinesTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 125 | The metric k-median approximation threshold and recoveryTheoretical computer science | Theoretical computer science | 2 | 4 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 4 of 4 | None recorded | No explanation yet |
| 126 | Exponential semidefinite complexity of perfect matchingTheoretical computer science | Theoretical computer science | 1 | 2 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | None recorded | No explanation yet |
| 127 | Average sensitivity of polynomial threshold functionsTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 128 | A factor-two approximation for shortest common superstringTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 129 | Exponential state costs for two-way automataTheoretical computer science | Theoretical computer science | 2 | 3 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | None recorded | No explanation yet |
| 130 | Exact Fourier transforms below \(n\log n\)Theoretical computer science | Theoretical computer science | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | Exact calculations for finite claims | Two explanations by others |
| 131 | Rapid mixing of graph switches for every degree sequenceTheoretical computer scienceThe two readers disagree | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 132 | A superquadratic separation of sensitivity and block sensitivityTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 133 | The computational complexity of Weisfeiler–Leman refinementTheoretical computer science | Theoretical computer science | 4 | 4 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 4 of 4 | None recorded | No explanation yet |
| 134 | Generalized star height at most threeTheoretical computer science | Theoretical computer science | 3 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 135 | Homogeneous depth-five lower bounds for iterated matrix multiplicationTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 136 | A quasilinear PCP theorem for PPADTheoretical computer science | Theoretical computer science | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 137 | One-tape time simulation in two-fifths-power spaceTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 138 | Subset Sum in \(O(2^{0.49n})\) timeTheoretical computer science | Theoretical computer science | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | No explanation yet |
| 139 | Subpolynomial query complexity for log-concave samplingTheoretical computer science | Theoretical computer science | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 140 | Memory–sample lower bounds for noiseless Gaussian regressionTheoretical computer science | Theoretical computer science | 6 | 8 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 8 of 8 | None recorded | No explanation yet |
| 141 | Existential–universal real sentences in the counting hierarchyTheoretical computer science | Theoretical computer science | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 142 | Deterministic polynomial factorization over prime fieldsTheoretical computer science | Theoretical computer science | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 143 | Hilbert’s sixteenth problem: uniform bounds for limit cyclesDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | One problem reported, not judged by the atlas |
| 144 | Banach’s simple Lebesgue-spectrum problemDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 145 | Rokhlin’s multiple-mixing problemDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 1 | 1 | 3 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | One problem reported, not judged by the atlas |
| 146 | Positive metric entropy for the standard mapDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 1 | 3 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | None recorded | No explanation yet |
| 147 | The near-boundary Birkhoff conjectureDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 148 | The entropy-rate dimension formula for self-similar measuresDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 149 | Classwise permanence for weakly reversible mass-action systemsDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 2 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 150 | Weak mixing of triangular billiards with an irrational angleDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 2 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | Proofs of selected steps in HOL Light | No explanation yet |
| 151 | A C1 counterexample to the entropy conjectureDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 152 | Zero entropy does not guarantee a smooth positive-volume modelDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 1 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 153 | Arithmetic classification and non-Pisot singularity for Bernoulli convolutionsDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | No explanation yet |
| 154 | Pointwise multiple ergodic averages for mixing transformationsDynamical systems and ergodic theory | Dynamical systems and ergodic theory | 4 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 155 | A counterexample to periodic tiling in dimension threeCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 156 | Borsuk’s conjecture fails in dimension nineCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | One explanation by others |
| 157 | Graph coloring, clique minors, and Colin de Verdière invariantsCombinatorics | Combinatorics | 3 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | Exact calculations for finite claims | No explanation yet |
| 158 | The Euclidean plane cannot be colored with five colorsCombinatorics | Combinatorics | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | Proofs of selected steps in HOL Light, exact calculations for finite claims | Two explanations by othersFour problems reported, not judged by the atlas |
| 159 | Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi boundsCombinatorics | Combinatorics | 1 | 1 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | One explanation by others |
| 160 | Superexponential van der Waerden numbersCombinatorics | Combinatorics | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 161 | Counterexamples to Sidorenko’s conjecture and the forcing conjectureCombinatorics | Combinatorics | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 162 | Counterexamples to Ryser’s covering conjectureCombinatorics | Combinatorics | 2 | 3 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 3 of 3 | Exact calculations for finite claims | No explanation yet |
| 164 | Hindman’s finite sums and products conjectureCombinatorics | Combinatorics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 165 | The Harary–Hill and Zarankiewicz crossing-number formulasCombinatorics | Combinatorics | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 166 | The higher-dimensional Erdős distinct-distances conjectureCombinatorics | Combinatorics | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 167 | Planar distinct distances and unit-distance boundsCombinatorics | Combinatorics | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 168 | Combinatorial invariance of Kazhdan–Lusztig polynomialsCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 169 | Shareshian–Wachs elementary positivityCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | Two problems reported, not judged by the atlas |
| 170 | Sharp logarithmic exponents for off-diagonal Ramsey numbersCombinatorics | Combinatorics | 2 | 2 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 171 | The hypercube Ramsey conjectureCombinatorics | Combinatorics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 172 | Classification of finite Euclidean Ramsey configurationsCombinatorics | Combinatorics | 1 | 7 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 7 of 7 | None recorded | No explanation yet |
| 173 | Seymour’s second-neighborhood conjectureCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 174 | Deterministic construction of strong thin spanning treesCombinatorics | Combinatorics | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 175 | Talagrand’s expectation thresholds, discrete convexity, and graph decompositionsCombinatorics | Combinatorics | 3 | 2 | 2 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | No explanation yet |
| 176 | The second Kahn–Kalai conjecture with an edge-count boundCombinatorics | Combinatorics | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 177 | Bounded-degree coboundary expandersCombinatoricsThe two readers disagree | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 178 | Deterministic nonbipartite Ramanujan graphs in every fixed degreeCombinatorics | Combinatorics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 179 | The circulant Hadamard and Barker-sequence conjecturesCombinatoricsThe two readers disagree | Combinatorics | 1 | 2 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | None recorded | No explanation yet |
| 180 | Barnette’s Hamiltonian-cycle conjectureCombinatoricsThe two readers disagree | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 181 | The Erdős–Gallai cycle-decomposition conjectureCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 182 | Power savings for intersective polynomial differences and prime argumentsCombinatorics | Combinatorics | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 183 | Power savings for planar halving lines and k-setsCombinatorics | Combinatorics | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 184 | Correspondence coloring with a fixed forbidden subgraphCombinatorics | Combinatorics | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 185 | Counterexamples to infinite matroid intersection and packing/coveringCombinatorics | Combinatorics | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 186 | Uniform influence and sharp thresholds for graph and hypergraph propertiesCombinatorics | Combinatorics | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 187 | Snaky in 21 Maker movesCombinatorics | Combinatorics | 1 | 3 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | Exact calculations for finite claims | No explanation yet |
| 188 | The sharp terminal leave in random triangle removalCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Proofs of selected steps in HOL Light | No explanation yet |
| 189 | Cycle–clique Ramsey numbersCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 0 of 1 | Exact calculations for finite claims | No explanation yet |
| 190 | Polynomial removal fails for ordered binary matricesCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 191 | A power improvement in the Heilbronn triangle lower boundCombinatorics | Combinatorics | 1 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 192 | Boolean functions violate the square-root degree bound by arbitrary factorsCombinatorics | Combinatorics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 193 | Serre’s intersection-multiplicity conjectureAlgebra | Algebra | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 194 | Lech’s multiplicity conjectureAlgebra | Algebra | 1 | 1 | 1 | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | No explanation yet |
| 195 | A counterexample to the small Cohen–Macaulay module conjectureAlgebra | Algebra | 1 | 1 | 1 | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “SUPPORT-ONLY” | 1 of 1 | None recorded | One explanation by others |
| 196 | A counterexample to Kaplansky’s zero-divisor conjectureAlgebra | Algebra | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Proofs of selected steps in HOL Light, exact calculations for finite claims | No explanation yet |
| 197 | A torsion-free group algebra that is not directly finiteAlgebra | Algebra | 4 | 4 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 4 of 4 | Exact calculations for finite claims | No explanation yet |
| 198 | A counterexample to finitistic-dimension finitenessAlgebra | Algebra | 1 | 2 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 199 | Counterexamples to Auslander–Reiten, Tachikawa and related homological conjecturesAlgebra | Algebra | 2 | 2 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | Exact calculations for finite claims | No explanation yet |
| 200 | Eisenbud–Green–Harris and lex-plus-powersAlgebra | Algebra | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 201 | A counterexample to Kurosh’s division-ring problemAlgebra | Algebra | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 202 | The blockwise Alperin weight conjectureAlgebra | Algebra | 1 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 203 | Donovan’s conjecture over fields and complete mixed-characteristic DVRsAlgebra | Algebra | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 204 | Tensor saturation for even spin groupsAlgebra | Algebra | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 205 | Saxl’s conjecture and universal tensor squaresAlgebra | Algebra | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 2 | Exact calculations for finite claims | No explanation yet |
| 206 | Finite lattice representation and undecidabilityAlgebra | Algebra | 2 | 1 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | No explanation yet |
| 207 | The ℓ¹-Bass conjecture for all discrete groupsAlgebra | Algebra | 2 | 2 | 1 | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNDECLARED” | 2 of 2 | None recorded | No explanation yet |
| 208 | Finite symmetric tensor categories and the Verlinde towerAlgebra | Algebra | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 209 | Integral counterexamples to Gersten’s conjectureAlgebra | Algebra | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 210 | Foulkes' conjecture for sixth powers and quadratic stabilizationAlgebra | Algebra | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 211 | The geometric phase diagram, diffusion, and spectra of random planar mapsProbability and statistical mechanics | Probability and statistical mechanics | 7 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 212 | Planar first-passage geometry and the absence of bigeodesicsProbability and statistical mechanics | Probability and statistical mechanics | 2 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | No explanation yet |
| 213 | Critical percolation on every quasi-transitive graphProbability and statistical mechanics | Probability and statistical mechanics | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | One explanation by others |
| 214 | The Benjamini–Schramm nonuniqueness conjectureProbability and statistical mechanics | Probability and statistical mechanics | 1 | 2 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 215 | Canonical \(O(3)\) continuum limit and exact \(O(4)\) mass asymptoticsProbability and statistical mechanics | Probability and statistical mechanics | 5 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 216 | Critical and near-critical XY scaling and BKT universalityProbability and statistical mechanics | Probability and statistical mechanics | 6 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 217 | The low-temperature Sherrington–Kirkpatrick fluctuation lawProbability and statistical mechanics | Probability and statistical mechanics | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 218 | Conformal universality for weakly interacting and random-bond Ising modelsProbability and statistical mechanics | Probability and statistical mechanics | 6 | 1 | 1 | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | One explanation by others |
| 219 | GOE bulk universality for regular graphs with weak Anderson disorderProbability and statistical mechanics | Probability and statistical mechanics | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 220 | Directional zero–one laws beyond iid environments and iid ballisticityProbability and statistical mechanics | Probability and statistical mechanics | 3 | 3 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 3 of 3 | None recorded | No explanation yet |
| 221 | The Mézard–Parisi formula for diluted spin glassesProbability and statistical mechanics | Probability and statistical mechanics | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | One explanation by others |
| 222 | Perceptron free energies and microscopic jamming exponentsProbability and statistical mechanics | Probability and statistical mechanics | 4 | 3 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 3 of 3 | Exact calculations for finite claims | No explanation yet |
| 223 | Random-cluster interfaces: critical, disordered, thermal, and natural-time scalingProbability and statistical mechanics | Probability and statistical mechanics | 6 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 224 | Critical and quenched near-critical universality for Poisson–Voronoi percolationProbability and statistical mechanics | Probability and statistical mechanics | 3 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 225 | Gaussian free field limits throughout the balanced six-vertex regimeProbability and statistical mechanics | Probability and statistical mechanics | 1 | No Lean statement | 4 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 226 | The double-dimer loop ensemble converges to CLE4Probability and statistical mechanics | Probability and statistical mechanics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 227 | Critical SK autocorrelation processes and dynamics across the temperature transitionProbability and statistical mechanics | Probability and statistical mechanics | 8 | 5 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 5 of 5 | Exact calculations for finite claims | No explanation yet |
| 228 | Continuum phase transitions for radial pair potentialsProbability and statistical mechanics | Probability and statistical mechanics | 2 | 3 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | None recorded | No explanation yet |
| 229 | Exact three- and four-state reconstruction thresholds and four-state tree capacityProbability and statistical mechanics | Probability and statistical mechanics | 3 | 2 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | Exact calculations for finite claims | No explanation yet |
| 230 | Exact Hausdorff gauges for SLEProbability and statistical mechanics | Probability and statistical mechanics | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 231 | The free uniform spanning forest is a factor of IIDProbability and statistical mechanics | Probability and statistical mechanics | 1 | 2 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 232 | Gaussian fields and interfaces for triangular-lattice Lipschitz heightsProbability and statistical mechanicsThree earlier editions | Probability and statistical mechanics | 3 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 233 | The joint critical Ashkin–Teller current limitProbability and statistical mechanicsOne earlier edition | Probability and statistical mechanics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 234 | All-temperature pressure of orthogonally invariant Ising spin glassesProbability and statistical mechanics | Probability and statistical mechanics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 235 | Limiting random SAT thresholds, sharp variance and computabilityProbability and statistical mechanics | Probability and statistical mechanics | 4 | 4 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 4 of 4 | None recorded | No explanation yet |
| 236 | The exact factor-of-IID threshold for free Ising spins on treesProbability and statistical mechanics | Probability and statistical mechanics | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 237 | The three-quarter exponent for honeycomb self-avoiding walkProbability and statistical mechanics | Probability and statistical mechanics | 13 | 4 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 4 of 4 | None recorded | No explanation yet |
| 238 | Optimal logarithmic mixing of the Thorp shuffleProbability and statistical mechanics | Probability and statistical mechanics | 12 | 13 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 13 of 13 | Exact calculations for finite claims | Four problems reported, not judged by the atlas |
| 239 | Sharp singularity rates for symmetric random sign matricesProbability and statistical mechanics | Probability and statistical mechanics | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 240 | Shelah’s eventual categoricity and the prescribed-threshold obstructionMathematical logic | Mathematical logic | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 241 | Rigidity of the Turing degreesMathematical logic | Mathematical logic | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 242 | Single-fold Diophantine representations and undecidability under an at-most-one-solution promiseMathematical logicThe two readers disagree | Mathematical logic | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 243 | Separating choiceless counting from polynomial time and witnessed choiceMathematical logic | Mathematical logic | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 244 | The Partition Principle does not imply ChoiceMathematical logic | Mathematical logic | 1 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | None recorded | No explanation yet |
| 245 | Weak normalization implies strong normalization in pure type systemsMathematical logic | Mathematical logic | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 246 | Cannon’s conjectureGroup theory | Group theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 247 | An infinite finitely presented residually finite 2-group and a finitely presented nil algebraGroup theory | Group theory | 2 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 248 | Thompson’s group F is nonamenableGroup theory | Group theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 249 | A finitely generated Eilenberg–Ganea counterexampleGroup theory | Group theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 250 | Boone–Higman embeddings with higher finitenessGroup theory | Group theory | 3 | 3 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | None recorded | No explanation yet |
| 251 | Amenability, unitarizability, and strong Ulam stabilityGroup theory | Group theory | 2 | 2 | 2 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | No explanation yet |
| 252 | A torsion-free hyperbolic group that is neither residually finite nor linear over any fieldGroup theoryThe two readers disagree | Group theory | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 253 | An infinite finitely presented simple amenable groupGroup theory | Group theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 254 | Classifying spaces and geometric obstructions for Artin groupsGroup theory | Group theory | 3 | 3 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 3 of 3 | None recorded | No explanation yet |
| 255 | Quasi-isometric recognition of virtually polycyclic groupsGroup theory | Group theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 256 | Nonsingular systems of equations over arbitrary groupsGroup theory | Group theory | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 257 | A hyperbolic group without a geometric CAT(0) actionGroup theory | Group theory | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 258 | Gersten’s conjecture and virtual compact specialness of one-relator groupsGroup theory | Group theory | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 259 | A group without fixed priceGroup theory | Group theory | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 260 | Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensionsMathematical physics | Mathematical physics | 13 | 1 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | Two explanations by others |
| 261 | Localization and delocalization in the Anderson modelMathematical physics | Mathematical physics | 2 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | One explanation by others |
| 262 | Sharp finite-matrix Lieb–Thirring inequalities and all equality casesMathematical physics | Mathematical physics | 3 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | One explanation by others |
| 263 | The ionization and generalized ionization conjecturesMathematical physics | Mathematical physics | 3 | 2 | 2 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | One explanation by others |
| 264 | Strong cosmic censorship near two-ended Kerr dataMathematical physics | Mathematical physics | 3 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | Two explanations by others |
| 265 | Area laws and tensor networks for two-dimensional gapped systemsMathematical physics | Mathematical physics | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 266 | Exactly three mutually unbiased bases in dimension sixMathematical physics | Mathematical physics | 2 | 2 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | Exact calculations for finite claims | Two explanations by othersOne problem reported, not judged by the atlas |
| 267 | Positive-temperature Bose–Einstein condensation and exact quantum depletionMathematical physics | Mathematical physics | 5 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | One explanation by others |
| 268 | The spin-one Haldane gapMathematical physics | Mathematical physics | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | Two explanations by others |
| 269 | Uniform Laughlin gap and stability under bounded scalar disorderMathematical physics | Mathematical physics | 2 | 4 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 4 of 4 | Exact calculations for finite claims | Two explanations by others |
| 270 | Threshold and positive-energy bound states of the BFSS matrix modelMathematical physics | Mathematical physics | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 271 | Bloch’s law, its lattice correction, and the spherical magnetization lawMathematical physics | Mathematical physics | 4 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | Two explanations by others |
| 272 | Entanglement without distillable secret keyMathematical physics | Mathematical physics | 1 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 2 of 2 | Exact calculations for finite claims | Two explanations by others |
| 273 | The entropy photon-number inequalityMathematical physicsThe two readers disagree | Mathematical physics | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | One explanation by others |
| 274 | Parity is not in QAC0Mathematical physicsThe two readers disagree | Mathematical physics | 2 | 2 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 2 of 2 | None recorded | Two explanations by others |
| 275 | QMA-hardness of continuum Coulomb energyMathematical physics | Mathematical physics | 2 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 0 of 1 | None recorded | Two explanations by others |
| 276 | Classical capacity of generalized amplitude dampingMathematical physics | Mathematical physics | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | Two explanations by others |
| 277 | Threshold repetition for entangled gamesMathematical physics | Mathematical physics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | One explanation by others |
| 278 | Failure of Kohn–Sham ensemble representationMathematical physics | Mathematical physics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 279 | Exact quantum factoring over a fixed finite gate setMathematical physics | Mathematical physics | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | Two explanations by others |
| 280 | Unitary vertex operator algebras and conformal netsMathematical physics | Mathematical physics | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | One explanation by others |
| 281 | QAOA attains the SK optimum in the thermodynamic-first limitMathematical physics | Mathematical physics | 2 | 2 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 2 of 2 | Exact calculations for finite claims | Two explanations by others |
| 282 | From scale symmetry to local conformal symmetry in four-dimensional QFTMathematical physics | Mathematical physics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 283 | Polynomial-time unitary synthesis from a Boolean oracleMathematical physics | Mathematical physics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 284 | The optimal quartic separation between randomized and quantum queriesMathematical physics | Mathematical physics | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | Two explanations by others |
| 285 | Counterexamples to Baum–Connes and Kadison–KaplanskyOperator algebras | Operator algebras | 3 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 286 | Rigidity and arithmetic of lattice von Neumann algebrasOperator algebras | Operator algebras | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 287 | Isomorphism of the free group factorsOperator algebrasThe two readers disagree | Operator algebras | 1 | 1 | 3 | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | One explanation by others |
| 288 | Kadison’s similarity conjectureOperator algebras | Operator algebras | 1 | 2 | 2 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 289 | Strong Kadison–Kastler stability and its spatial boundariesOperator algebras | Operator algebras | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 290 | Relative bicentralizers and modular spectral recoveryOperator algebras | Operator algebras | 2 | 1 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | No explanation yet |
| 291 | Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stabilityOperator algebras | Operator algebras | 4 | 1 | 2 | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | No explanation yet |
| 292 | Kirchberg’s \(\mathcal O_2\) norm-ultrapower embedding problemOperator algebras | Operator algebras | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 293 | Invariant projections, hyperinvariant subspaces, and transitive algebrasOperator algebras | Operator algebras | 2 | 6 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 6 of 6 | None recorded | No explanation yet |
| 294 | Kaplansky’s quasitrace conjecture and failure of tensor-product stable finitenessOperator algebras | Operator algebras | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 295 | The Kadison–Ringrose cohomology conjectureOperator algebras | Operator algebras | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 296 | The generator problem for finite factorsOperator algebras | Operator algebras | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 297 | A ZFC counterexample to Naimark’s problemOperator algebras | Operator algebras | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | One explanation by othersTwo problems reported, not judged by the atlas |
| 298 | Two notions of free entropy differ even when both are finiteOperator algebras | Operator algebras | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 299 | The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stabilityOperator algebras | Operator algebras | 1 | 1 | 1 | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 300 | Approximation and quadratic strong-operator pavingOperator algebras | Operator algebras | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 301 | Trace cones and Razak–Jacelon stabilizationOperator algebras | Operator algebras | 1 | 1 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “SUPPORT-ONLY” | 1 of 1 | None recorded | No explanation yet |
| 302 | Radius of comparison equals half the mean dimensionOperator algebras | Operator algebras | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 303 | Weak pure infiniteness and Cuntz-algebra absorptionOperator algebrasThe two readers disagree | Operator algebras | 1 | 2 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 2 of 2 | None recorded | No explanation yet |
| 304 | The Hilbert–Smith conjecture in every dimensionTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | Two explanations by others |
| 305 | Four-dimensional disk embedding and Wall’s conjectureTopology | Topology | 3 | No Lean statement | 2 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 306 | The purely cosmetic surgery conjectureTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 307 | Failure of rational injectivity for maximal coarse assemblyTopology | Topology | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 0 of 1 | None recorded | No explanation yet |
| 308 | Finite Smith–Toda complexes at every heightTopology | Topology | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 309 | The Kervaire invariant problem at the prime threeTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | No explanation yet |
| 310 | Quillen’s conjecture in rational homologyTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 311 | The Hovey–Strickland and Chai conjecturesTopology | Topology | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 312 | The Grothendieck homotopy hypothesisTopology | Topology | 1 | 1 | 1 | A supporting or different resultTheir term: “supporting-only” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | One explanation by othersOne problem reported, not judged by the atlas |
| 313 | Finite generation for the \(K(n)\)-local sphereTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 314 | Cyclic length and chromatic fixed-point lossTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 315 | The four-dimensional Singer conjectureTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 316 | Curtis’s conjectureTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 317 | Thomason model structures in all strict higher dimensionsTopology | Topology | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 318 | Chromatic splitting: filtrations and counterexamplesTopology | Topology | 5 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 319 | Counterexamples to finite generation at chromatic height twoTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 320 | Nonhomeomorphic closed aspherical four-manifoldsTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 321 | A counterexample to Wall’s finite D(2) problemTopology | Topology | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 322 | Tingley’s sphere-isometry problemFunctional analysis | Functional analysis | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 323 | Independence of the separable quotient problemFunctional analysis | Functional analysis | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 324 | Lipschitz equivalent Banach spaces need not be linearly isomorphicFunctional analysis | Functional analysis | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 325 | The complete Crouzeix conjectureFunctional analysis | Functional analysis | 2 | 5 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 5 of 5 | Proofs of selected steps in HOL Light | One explanation by othersOne problem reported, not judged by the atlas |
| 326 | The cotype–cotype conjecture under the approximation propertyFunctional analysisThe two readers disagree | Functional analysis | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — UNDECLARED” | 1 of 1 | None recorded | No explanation yet |
| 327 | Markov type characterizes superreflexivityFunctional analysis | Functional analysis | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 328 | Nonexpansive fixed points in reflexive Banach spacesFunctional analysis | Functional analysis | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 329 | A counterexample to metric-entropy dualityFunctional analysis | Functional analysis | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 330 | A uniformly discrete counterexample to bounded approximation in Lipschitz-free spacesFunctional analysis | Functional analysis | 1 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 331 | Reflexive midpoint convexity and diamond distortionFunctional analysis | Functional analysis | 7 | 7 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 7 of 7 | None recorded | No explanation yet |
| 332 | Metric Markov cotype of ℓ1 and Hilbert-space Lipschitz extensionFunctional analysis | Functional analysis | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 333 | Smooth isometric immersions of surfaces into ℝ4Differential geometry | Differential geometry | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 334 | A smooth surface metric with no local isometric immersion in ℝ3Differential geometry | Differential geometry | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 335 | Gromov’s integral scalar-curvature bound for simplicial volumeDifferential geometry | Differential geometry | 2 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | One problem reported, not judged by the atlas |
| 336 | Spectral scalar curvature, Urysohn width, and macroscopic dimensionDifferential geometry | Differential geometry | 3 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One problem reported, not judged by the atlas |
| 337 | Sharp Cartan–Hadamard isoperimetry and rigidityDifferential geometry | Differential geometry | 2 | 2 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 2 of 2 | None recorded | No explanation yet |
| 338 | Yau’s uniformization conjectureDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 339 | Katok’s entropy rigidity conjectureDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 340 | A counterexample to the nearby Lagrangian conjectureDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 341 | Donaldson’s hypersymplectic deformation conjectureDifferential geometryOne earlier edition | Differential geometry | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 342 | Donaldson’s tamed-to-compatible conjectureDifferential geometryOne earlier edition | Differential geometry | 1 | 1 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 343 | Symplectic ball packing in higher dimensionsDifferential geometry | Differential geometry | 1 | 2 | 1 | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 344 | The metric Blaschke conjectureDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 345 | Infinitely many closed geodesics on Riemannian spheres and closed three-manifoldsDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 346 | Sharp singular-set bounds for stationary integral varifoldsDifferential geometry | Differential geometry | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 347 | Counterexamples to stable-Morse and strong Arnold fixed-point boundsDifferential geometry | Differential geometry | 5 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 348 | Nonnegative-curvature Einstein classification and an L2 topological gapDifferential geometry | Differential geometry | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 349 | The Solomon–Yau least-volume conjectureDifferential geometry | Differential geometry | 1 | No Lean statement | 1 | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 350 | Yau’s nodal bounds: surfaces and higher dimensionsDifferential geometry | Differential geometry | 3 | 3 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNDECLARED” | 3 of 3 | None recorded | No explanation yet |
| 351 | Scalar curvature and finite-time Ricci-flow singularitiesDifferential geometry | Differential geometry | 3 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 352 | A finite-time singularity of Calabi flowDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | Exact calculations for finite claims | No explanation yet |
| 353 | Affine Bernstein rigidity through dimension nine and a smooth dimension-ten counterexampleDifferential geometry | Differential geometry | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | Proofs of selected steps in HOL Light | No explanation yet |
| 354 | The isoperimetric profile of the cubic three-torusDifferential geometry | Differential geometry | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Proofs of selected steps in HOL Light, exact calculations for finite claims | No explanation yet |
| 355 | Unique tangent flows at the first surface singularityDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 356 | Gigli’s characterization of Alexandrov curvatureDifferential geometry | Differential geometry | 2 | 1 | Not cited | A supporting or different resultTheir term: “supporting-only” | A supporting or different resultTheir term: “DIFFERENT” | 1 of 1 | None recorded | No explanation yet |
| 357 | Bi-Lipschitz coordinates at every regular RCD pointDifferential geometry | Differential geometry | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 358 | A three-manifold without conjugate points or nonpositive curvatureDifferential geometry | Differential geometry | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 359 | Negative Kähler curvature without bounded holomorphic coordinatesDifferential geometry | Differential geometry | 2 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 360 | Weak MTW curvature gives convexity and regular optimal transportDifferential geometry | Differential geometry | 2 | 2 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 2 of 2 | None recorded | No explanation yet |
| 361 | Failure of integer-degree harmonic dimension comparisonDifferential geometry | Differential geometry | 2 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 362 | Global smoothness for relativistic Vlasov–MaxwellPartial differential equations | Partial differential equations | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | One explanation by others |
| 363 | Nonuniqueness with local conservation for the hard-sphere Boltzmann equationPartial differential equations | Partial differential equations | 2 | 1 | Not cited | Part of itTheir term: “weaker-statement” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 364 | Kinetic limits and fluctuations over the Boltzmann lifespanPartial differential equations | Partial differential equations | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 365 | Joint metric and connection recovery from one boundary patchPartial differential equations | Partial differential equations | 3 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — UNLINKED” | 1 of 1 | None recorded | No explanation yet |
| 366 | The planar Mumford–Shah regularity conjecture and local weak-L4 gradient boundsPartial differential equations | Partial differential equations | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 367 | The critical dimension for the one-phase Bernoulli problemPartial differential equations | Partial differential equations | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | Exact calculations for finite claims | No explanation yet |
| 368 | The three-dimensional Ball–Evans approximation problemPartial differential equations | Partial differential equations | 2 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
| 369 | The hot spots conjecture for simply connected planar domainsPartial differential equations | Partial differential equations | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | Proofs of selected steps in HOL Light | No explanation yet |
| 370 | The Lane–Emden and Hénon–Lane–Emden conjecturesPartial differential equations | Partial differential equations | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 371 | Stable blowup for the defocusing Schrödinger equationPartial differential equationsThe two readers disagree | Partial differential equations | 1 | 1 | Not cited | All of itTheir term: “full” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | Exact calculations for finite claims | One problem reported, not judged by the atlas |
| 372 | Global uniqueness in smooth isotropic elasticityPartial differential equations | Partial differential equations | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | No explanation yet |
| 373 | Nonattainment of the three-marginal Coulomb Monge problemPartial differential equations | Partial differential equations | 1 | 1 | Not cited | Part of itTheir term: “partial” | Part of itTheir term: “NARROWER — DECLARED” | 1 of 1 | None recorded | No explanation yet |
| 374 | Sharp one-third stability of Brenier mapsPartial differential equations | Partial differential equations | 1 | 1 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 1 of 1 | None recorded | One problem reported, not judged by the atlas |
| 375 | De Giorgi’s conjecture in dimension eightPartial differential equations | Partial differential equations | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | One explanation by others |
| 376 | Universal computation in forced Navier–Stokes flowsPartial differential equationsOne earlier edition | Partial differential equations | 9 | 6 | Not cited | All of itTheir term: “full” | All of itTheir term: “MATCHES” | 6 of 6 | None recorded | One explanation by others |
| 377 | Interior \(C^{1,\alpha}\) regularity for infinity-harmonic functionsPartial differential equations | Partial differential equations | 1 | No Lean statement | Not cited | No Lean statement | No Lean statement | No Lean statement | None recorded | No explanation yet |
Where a careful reading is most useful
The first 25 of the 172 Lean statements with a specific reason for a careful reading, each with its reasons.
- Elementary positivity for natural unit interval graphs Family 169: Shareshian–Wachs elementary positivity
- The configuration names no theorem: it checks a definition whose type carries the claim, so read that definition's type and body.
- 1 definition hole: Comparator compares it by name and type only, so a reader checks what each solution body means.
- Nine routing-density and representation estimates Family 238: Optimal logarithmic mixing of the Thorp shuffle
- The AI draft scope reading could not tell from OpenAI's note how much of a paper's theorem this file states.
- The draft scope reading depends on mathematics a specialist should settle.
- 357 local vocabulary declarations to read.
- Exact equality of deterministic and randomized logarithmic space Family 103: Exact derandomization of logarithmic space: \(\mathsf L=\mathsf{RL}=\mathsf{BPL}\)
- 20 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Stable self-similar blowup and positive-probability Gaussian blowup Family 371: Stable blowup for the defocusing Schrödinger equation
- 3 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Counterexample to harmonic dimension comparison Family 361: Failure of integer-degree harmonic dimension comparison
- Both independent readers find this family's challenges state less than its headline, while the atlas's AI draft classes this file as stating a paper's theorem as the paper does; check which part of the headline it covers.
- States its claim through an axiom in the challenge file; check what the configuration compares.
- One-third stability of Brenier maps and sharpness Family 374: Sharp one-third stability of Brenier maps
- 12 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- Squared-logarithmic randomized $k$-server on arbitrary metrics Family 110: Optimal-order randomized k-server on arbitrary metrics
- 9 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- Counterexample to Naimark's problem in ZFC Family 297: A ZFC counterexample to Naimark’s problem
- 7 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- Area-controlled end replacement and Schwarzschild equality examples Family 260: Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensions
- Both independent readers find this family's challenges state less than its headline, while the atlas's AI draft classes this file as stating a paper's theorem as the paper does; check which part of the headline it covers.
- 310 local vocabulary declarations to read.
- Row–column overlap on occupied boards Family 238: Optimal logarithmic mixing of the Thorp shuffle
- 5 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- Failure of rational injectivity for ordinary coarse assembly Family 307: Failure of rational injectivity for maximal coarse assembly
- Both independent readers find this family's challenges state less than its headline, while the atlas's AI draft classes this file as stating a paper's theorem as the paper does; check which part of the headline it covers.
- 216 local vocabulary declarations to read.
- Mixing of every finite order for one mixing transformation Family 145: Rokhlin’s multiple-mixing problem
- 4 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- Kirchberg–Rørdam character criterion Family 299: The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stability
- Both independent readers find this family's challenges state less than its headline, while the atlas's AI draft classes this file as stating a paper's theorem as the paper does; check which part of the headline it covers.
- 146 local vocabulary declarations to read.
- One-sided angle bound for signed spin types Family 238: Optimal logarithmic mixing of the Thorp shuffle
- 3 definition holes: Comparator compares these by name and type only, so a reader checks what each solution body means.
- No proper five-coloring Family 158: The Euclidean plane cannot be colored with five colors
- 1 definition hole: Comparator compares it by name and type only, so a reader checks what each solution body means.
- Perfect-matching entropy bound Family 113: Approximate counting and entropy of perfect matchings
- The draft scope reading depends on mathematics a specialist should settle.
- Projection estimates and memory–precision bounds Family 140: Memory–sample lower bounds for noiseless Gaussian regression
- The draft scope reading depends on mathematics a specialist should settle.
- Barnette's Hamiltonian-cycle conjecture Family 180: Barnette’s Hamiltonian-cycle conjecture
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Bounded-treewidth graph metrics in $L_1$ Family 089: Bounded-distortion L1 embeddings of planar and bounded-treewidth graphs
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Brennan and inverse-square integral-means bounds Family 072: Brennan’s conjecture and the integral-means spectrum
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Sharp endpoint divergence Family 072: Brennan’s conjecture and the integral-means spectrum
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Classification of circulant Hadamard orders Family 179: The circulant Hadamard and Barker-sequence conjectures
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Bounded-degree coboundary expanders in dimensions at least three Family 177: Bounded-degree coboundary expanders
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Cotype–cotype equivalence with approximation property Family 326: The cotype–cotype conjecture under the approximation property
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
- Entropy photon-number inequality for finite-energy bosonic inputs Family 273: The entropy photon-number inequality
- Two independent readers, MathVet and cert-machine, disagree on whether this family's challenges state its headline; a specialist reading would settle it.
Points per reason, highest first: a configuration with no theorem target 100; definition holes 90 plus one per hole; unclear draft scope 85; a draft scope reading needing a specialist 80; independent readers disagreeing on the family 75; both independent readers finding less than the headline where the atlas's AI draft says the file states a paper's theorem as the paper does 72; a target theorem shared with another file 70; an axiom in the challenge 60; no local vocabulary but OpenAI imports 50; 100 or more local declarations 20 plus one per hundred (capped); a family in which the AI draft finds no statement of a paper's theorem as the paper does 5. Ties go alphabetically. The order allocates reading; it is no verdict.
The order allocates reading time and says nothing about whether any statement or proof is correct.