draw_rank,family_id,paper_title,pdf_url,pdf_bytes,tex_file_count,readme_url,contents_url,lean_scope_url,status,representative_catalogue_url,catalogued_companion_titles,candidate_comparators,checker_execution,proof_content_inspected
18,015,Equidistribution of Prime-Degree Torus Packets with Arbitrary Local Type,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/paper.pdf,404189,7,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L411,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/015.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/DukePrimeDegree.json,not_run,False
2,024,An asymptotic formula for the number of totients,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/An-asymptotic-formula-for-the-number-of-totients-September-25-2026.pdf,563178,8,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L618,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/024.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/TotientAsymptotic.json | lean/ComparatorChallenges/TotientCompanionZero.json,not_run,False
7,046,A projective fourfold with large fundamental group and non-Stein universal cover,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/large-fundamental-group-non-stein.pdf,593161,12,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L1233,,no_family_lean_link_found,,,,not_run,False
15,065,Virasoro Constraints under Projectivization,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf,539629,11,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L1629,,no_family_lean_link_found,,,,not_run,False
5,082,Annular variation of the triangular Hilbert transform at the symmetric point,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/annular-variation.pdf,523253,10,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L2020,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/082.md,companion_listed_representative_unresolved,,The maximal triangular Hilbert transform at the symmetric point,lean/ComparatorChallenges/TriangularHilbert.json,not_run,False
9,113,A Fully Polynomial Randomized Approximation Scheme for Perfect Matchings in General Graphs,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/main.pdf,617073,1,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L2768,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/113.md,companion_listed_representative_unresolved,,Entropy and Face Dimension of the Perfect-Matching Polytope,lean/ComparatorChallenges/MatchingFPRAS.json | lean/ComparatorChallenges/MatchingEntropy.json,not_run,False
13,115,Exact Uniform Sampling of Contingency Tables with Arbitrary Margins,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/main.pdf,525125,9,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L2822,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/115.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/ContingencyTables.json,not_run,False
4,127,Average sensitivity of polynomial threshold functions,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/main.pdf,354487,9,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L3070,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/127.md,representative_listed,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/formalization.yaml#L304,,lean/ComparatorChallenges/GotsmanLinial.json,not_run,False
6,148,The entropy-rate dimension formula for self-similar measures on the line,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/main.pdf,416553,7,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L3541,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/148.md,representative_listed,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/formalization.yaml#L724,,lean/ComparatorChallenges/SelfSimilar.json | lean/ComparatorChallenges/SelfSimilarCorollaries.json,not_run,False
1,154,Pointwise Multiple Ergodic Averages for Mixing Transformations,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/multiple-ergodic-averages.pdf,435847,9,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L3655,,no_family_lean_link_found,,,,not_run,False
10,164,Monochromatic finite sums and products in the positive integers,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/paper.pdf,775466,10,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L3861,,no_family_lean_link_found,,,,not_run,False
20,192,Unbounded Violations of the Square-Root Degree Bound,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026.pdf,373964,9,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L4407,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/192.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/SquareRootDegree.json,not_run,False
19,210,Foulkes' conjecture for the sixth symmetric power,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/main.pdf,451463,8,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L4789,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/210.md,companion_listed_representative_unresolved,,Quadratic stabilization of the canonical Foulkes--Howe map,lean/ComparatorChallenges/FoulkesHowe.json,not_run,False
14,215,The canonical massive continuum limit of the two-dimensional O(3) model,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf,1036781,21,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L4950,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/215.md,companion_listed_representative_unresolved,,Exponential decay in two-dimensional classical O(n) models,lean/ComparatorChallenges/ClassicalON.json,not_run,False
3,230,An exact Hausdorff gauge for SLE,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/An-exact-Hausdorff-gauge-for-SLE-September-25-2026.pdf,561334,12,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L5548,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/230.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/SLELowerPositivity.json,not_run,False
17,245,Weak and strong normalization in pure type systems,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/paper.pdf,719425,11,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L6078,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/245.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/TypeSystemNormalization.json,not_run,False
16,296,Relative generation and the generator problem for finite factors,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf,205670,7,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L7366,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/296.md,representative_listed,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/formalization.yaml#L579,,lean/ComparatorChallenges/FactorGeneration.json | lean/ComparatorChallenges/RelativeGeneration.json,not_run,False
11,351,A closed Ricci flow with bounded scalar curvature and finite-time curvature blowup,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/paper.pdf,221862,10,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L8533,,no_family_lean_link_found,,,,not_run,False
12,369,Strict hot spots and absence of interior critical points on smooth simply connected planar domains,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/main.pdf,390272,8,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L8929,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/369.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/HotSpots.json,not_run,False
8,372,Global Uniqueness for the Smooth Isotropic Elasticity Inverse Problem,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/article.pdf,426737,7,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/README.md,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L8977,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/372.md,family_lean_link_scope_unresolved,,,lean/ComparatorChallenges/ElasticityUniqueness.json,not_run,False
