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| version: "v0.4" |
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| project: |
| name: "OpenAI math repository" |
| description: "Lean formalizations accompanying a mathematics manuscript collection." |
| authors: ["OpenAI"] |
| license: "Apache-2.0" |
|
|
| sources: |
| - title: "$L_1$ Embeddings of Graphs of Bounded Treewidth" |
| authors: ["OpenAI"] |
| id: ../preprints/L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A CH obstruction to a prescribed categoricity threshold" |
| authors: ["OpenAI"] |
| id: ../preprints/A-CH-Obstruction-to-a-Prescribed-Categoricity-Threshold-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A classification of finite Euclidean Ramsey configurations" |
| authors: ["OpenAI"] |
| id: ../preprints/A-classification-of-finite-Euclidean-Ramsey-configurations-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A Complete Local Domain without a Small Cohen–Macaulay Module" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A continuum temperature singularity for a radial pair potential" |
| authors: ["OpenAI"] |
| id: ../preprints/A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A counterexample to Hadwiger's conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/A-counterexample-to-Hadwigers-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A counterexample to integer-degree harmonic dimension comparison" |
| authors: ["OpenAI"] |
| id: ../preprints/A-counterexample-to-integer-degree-harmonic-dimension-comparison-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Characteristic Two" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Odd Characteristic" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026/paper.pdf |
| type: article |
|
|
| - title: "A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness" |
| authors: ["OpenAI"] |
| id: ../preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A counterexample to Ryser's covering conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Counterexample-to-Rysers-Covering-Conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A counterexample to Tachikawa's second conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A Counterexample to the Group-Ring Determinant Conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A Counterexample to the Infinite Matroid Packing/Covering Conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A Cyclic Polytabloid Proof of Saxl's Conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A Direct Proof of Optimal Max-Cut Hardness" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Direct-Proof-of-Optimal-Max-Cut-Hardness-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A direct proof of the complete Crouzeix inequality" |
| authors: ["OpenAI"] |
| id: ../preprints/A-direct-proof-of-the-complete-Crouzeix-inequality-September-26-2026/paper.pdf |
| type: article |
|
|
| - title: "A doubling Hilbert subset with no finite-dimensional bi-Lipschitz embedding" |
| authors: ["OpenAI"] |
| id: ../preprints/A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026/main.pdf |
| type: article |
|
|
| - title: "A Fock-space inequality and the Laughlin spectral gap" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026.pdf |
| type: article |
|
|
| - title: "A hyperbolic group with no geometric CAT(0) action" |
| authors: ["OpenAI"] |
| id: ../preprints/A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "A linear cycle-and-edge decomposition of every graph" |
| authors: ["OpenAI"] |
| id: ../preprints/A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026/main.pdf |
| type: article |
|
|
| - title: "A logarithmic independence bound for clique-free graphs" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Logarithmic-Independence-Bound-for-Clique-Free-Graphs-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "A negatively pinched Kähler threefold without bounded holomorphic coordinates" |
| authors: ["OpenAI"] |
| id: ../preprints/A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "A nine-dimensional counterexample to Borsuk's covering assertion" |
| authors: ["OpenAI"] |
| id: ../preprints/A-nine-dimensional-counterexample-to-Borsuks-covering-assertion-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A nonspectrahedral hyperbolicity cone" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026/nonspectrahedral-hyperbolicity-cone.pdf |
| type: article |
|
|
| - title: "A Polynomial-Time 2-Approximation for Shortest Common Superstring" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A positive solution to Tingley's problem" |
| authors: ["OpenAI"] |
| id: ../preprints/A-positive-solution-to-Tingleys-problem-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A product counterexample to the simplex maximum for projection-body volume" |
| authors: ["OpenAI"] |
| id: ../preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A proof of Seymour’s second-neighborhood conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A quadratic bound for Jacobsthal's function" |
| authors: ["OpenAI"] |
| id: ../preprints/A-quadratic-bound-for-Jacobsthals-function-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "A radial continuum phase transition with algebraic decay" |
| authors: ["OpenAI"] |
| id: ../preprints/A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A single-lattice covering bound of order n log n" |
| authors: ["OpenAI"] |
| id: ../preprints/A-single-lattice-covering-bound-of-order-n-log-n-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A Smooth Metric with No Local Isometric Immersion into Three-Space" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A stable coordinate that is not a coordinate in four variables" |
| authors: ["OpenAI"] |
| id: ../preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf |
| type: article |
|
|
| - title: "A strict inverse-first-power bound for univalent functions" |
| authors: ["OpenAI"] |
| id: ../preprints/A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A superquadratic separation between sensitivity and block sensitivity" |
| authors: ["OpenAI"] |
| id: ../preprints/A-superquadratic-separation-between-sensitivity-and-block-sensitivity-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "A Torsion-Free Group Algebra with Zero Divisors" |
| authors: ["OpenAI"] |
| id: ../preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A torsion-free hyperbolic group that is not residually finite" |
| authors: ["OpenAI"] |
| id: ../preprints/a-torsion-free-hyperbolic-group-that-is-not-residually-finite-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A translational tile with no fully periodic tiling in dimension three" |
| authors: ["OpenAI"] |
| id: ../preprints/A-translational-tile-with-no-fully-periodic-tiling-in-dimension-three-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "A universal group of type F∞" |
| authors: ["OpenAI"] |
| id: ../preprints/A-universal-group-of-type-F-infinity-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Additive hardness and unbounded configuration gaps in bin packing" |
| authors: ["OpenAI"] |
| id: ../preprints/Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026/Additive-hardness-and-unbounded-configuration-gaps-in-bin-packing-September-24-2026.pdf |
| type: article |
|
|
| - title: "Almost-everywhere Fourier convergence in L log L" |
| authors: ["OpenAI"] |
| id: ../preprints/Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Ample rank-two bundles on the quadric surface without Griffiths-positive metrics" |
| authors: ["OpenAI"] |
| id: ../preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "An algebra of infinite little finitistic dimension" |
| authors: ["OpenAI"] |
| id: ../preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "An Artin group with no geometric CAT(0) action" |
| authors: ["OpenAI"] |
| id: ../preprints/An-Artin-group-with-no-geometric-CAT-0-action-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "An Endpoint Gradient Bound for the Centered Disk Maximal Operator" |
| authors: ["OpenAI"] |
| id: ../preprints/An-Endpoint-Gradient-Bound-for-the-Centered-Disk-Maximal-Operator-September-26-2026/article.pdf |
| type: article |
|
|
| - title: "An explicit counterexample to the Auslander-Reiten conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "An explicit failure of complex affine-space cancellation" |
| authors: ["OpenAI"] |
| id: ../preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "An explicit noncoordinate polynomial with affine three-space zero fibre" |
| authors: ["OpenAI"] |
| id: ../preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "An explicit power saving for the exact discrete Fourier transform" |
| authors: ["OpenAI"] |
| id: ../preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026/main.pdf |
| type: article |
|
|
| - title: "An exponential state lower bound for two-way nondeterministic complementation" |
| authors: ["OpenAI"] |
| id: ../preprints/An-exponential-state-lower-bound-for-two-way-nondeterministic-complementation-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "An exponential two-way deterministic state lower bound for one-way liveness" |
| authors: ["OpenAI"] |
| id: ../preprints/An-exponential-two-way-deterministic-state-lower-bound-for-one-way-liveness-September-25-2026/main.pdf |
| type: article |
|
|
| - title: "An infinite finitely presented simple amenable group" |
| authors: ["OpenAI"] |
| id: ../preprints/An-Infinite-Finitely-Presented-Simple-Amenable-Group-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "An Upper Bound of 9/4 for the Matrix Multiplication Exponent" |
| authors: ["OpenAI"] |
| id: ../preprints/Matrix-Multiplication-Nine-Fourths-October-2-2026/paper.pdf |
| type: article |
|
|
| - title: "Approximate counting of common bases of two matroids" |
| authors: ["OpenAI"] |
| id: ../preprints/Approximate-counting-of-common-bases-of-two-matroids-September-23-2026/main.pdf |
| type: article |
|
|
| - title: "Asymptotic midpoint uniform convexity and unbounded diamond distortion in a reflexive tree space" |
| authors: ["OpenAI"] |
| id: ../preprints/Asymptotic-midpoint-uniform-convexity-and-unbounded-diamond-distortion-in-a-reflexive-tree-space-September-27-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Asymptotically minimal maxima of real Littlewood polynomials" |
| authors: ["OpenAI"] |
| id: ../preprints/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Average sensitivity of polynomial threshold functions" |
| authors: ["OpenAI"] |
| id: ../preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/main.pdf |
| type: article |
|
|
| - title: "Backward intertwiners and a transitive commutant" |
| authors: ["OpenAI"] |
| id: ../preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf |
| type: article |
|
|
| - title: "Beyond the Square-Root Exponent for Depth-Three Boolean Circuits" |
| authors: ["OpenAI"] |
| id: ../preprints/Beyond-the-Square-Root-Exponent-for-Depth-Three-Boolean-Circuits-September-23-2026/main.pdf |
| type: article |
|
|
| - title: "Bi-Lipschitz Absorption of $c_0$ Without a Linear Copy of $c_0$" |
| authors: ["OpenAI"] |
| id: ../preprints/Bi-Lipschitz-Absorption-of-c0-Without-a-Linear-Copy-of-c0-September-26-2026/paper.pdf |
| type: article |
|
|
| - title: "Bounded recovery for modular spectral averages" |
| authors: ["OpenAI"] |
| id: ../preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026/Bounded-recovery-for-modular-spectral-averages-September-23-2026.pdf |
| type: article |
|
|
| - title: "Bounded-Step Walks on Gaussian Primes" |
| authors: ["OpenAI"] |
| id: ../preprints/Bounded-Step-Walks-on-Gaussian-Primes-September-26-2026/paper.pdf |
| type: article |
|
|
| - title: "Brennan's conjecture and sharp inverse-square integral means" |
| authors: ["OpenAI"] |
| id: ../preprints/Brennans-conjecture-and-sharp-inverse-square-integral-means-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Choiceless polynomial time with counting does not capture polynomial time" |
| authors: ["OpenAI"] |
| id: ../preprints/Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Classical capacity and entropy inequalities for generalized amplitude damping" |
| authors: ["OpenAI"] |
| id: ../preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Compatibility entropy and the spectrum of a Thorp sweep" |
| authors: ["OpenAI"] |
| id: ../preprints/Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep-September-26-2026/paper.pdf |
| type: article |
|
|
| - title: "Complex Matrix Multiplication Below 2.258 and Rectangular Bounds" |
| authors: ["OpenAI"] |
| id: ../preprints/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026/Complex-Matrix-Multiplication-Below-2.258-and-Rectangular-Bounds-September-24-2026.pdf |
| type: article |
|
|
| - title: "Conditional coordinate sweeps and analytic transfer" |
| authors: ["OpenAI"] |
| id: ../preprints/Conditional-coordinate-sweeps-and-analytic-transfer-September-26-2026/main.pdf |
| type: article |
|
|
| - title: "Counterexamples to the duality conjecture for metric entropy" |
| authors: ["OpenAI"] |
| id: ../preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/main.pdf |
| type: article |
|
|
| - title: "Critical bond and site percolation on the cubic lattice" |
| authors: ["OpenAI"] |
| id: ../preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Critical honeycomb chords with prescribed boundary endpoints" |
| authors: ["OpenAI"] |
| id: ../preprints/Critical-honeycomb-chords-with-prescribed-boundary-endpoints-September-26-2026/main.pdf |
| type: article |
|
|
| - title: "Critical slowing down in the Sherrington–Kirkpatrick model" |
| authors: ["OpenAI"] |
| id: ../preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Directional transience implies ballisticity" |
| authors: ["OpenAI"] |
| id: ../preprints/Directional-transience-implies-ballisticity-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Distortion of countably branching diamonds from midpoint and tree energies" |
| authors: ["OpenAI"] |
| id: ../preprints/Diamond-distortion-from-midpoint-and-tree-energies-September-27-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Entropy and Face Dimension of the Perfect-Matching Polytope" |
| authors: ["OpenAI"] |
| id: ../preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/main.pdf |
| type: article |
|
|
| - title: "Exact asymptotic moduli in a Daugavet subspace of L1" |
| authors: ["OpenAI"] |
| id: ../preprints/Exact-asymptotic-moduli-in-a-Daugavet-subspace-of-L1-September-27-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Exact derandomization of logarithmic space: L = RL = BPL" |
| authors: ["OpenAI"] |
| id: ../preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Exponential decay in two-dimensional classical O(n) models" |
| authors: ["OpenAI"] |
| id: ../preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Finite tensor savings and exact Fourier circuits" |
| authors: ["OpenAI"] |
| id: ../preprints/Finite-tensor-savings-and-exact-Fourier-circuits-September-25-2026/main.pdf |
| type: article |
|
|
| - title: "Fixed Points of Nonexpansive Maps in Reflexive Banach Spaces" |
| authors: ["OpenAI"] |
| id: ../preprints/Fixed-Points-of-Nonexpansive-Maps-in-Reflexive-Banach-Spaces-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Generalized ionization energies for full Coulomb atoms" |
| authors: ["OpenAI"] |
| id: ../preprints/Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Global classical solutions of the three-dimensional relativistic Vlasov–Maxwell system" |
| authors: ["OpenAI"] |
| id: ../preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Global Support and Convex Injectivity Domains under Weak MTW" |
| authors: ["OpenAI"] |
| id: ../preprints/Global-Support-and-Convex-Injectivity-Domains-under-Weak-MTW-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "Hardness of finding large independent sets in three-colorable graphs" |
| authors: ["OpenAI"] |
| id: ../preprints/Hardness-of-finding-large-independent-sets-in-three-colorable-graphs-September-24-2026/Hardness-of-finding-large-independent-sets-in-three-colorable-graphs-September-24-2026.pdf |
| type: article |
|
|
| - title: "Harmonic heights and the Artin K(π,1) conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/Harmonic-heights-and-the-Artin-K-pi-1-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Independent products in real L1: asymptotic midpoint convexity without AUC renormings" |
| authors: ["OpenAI"] |
| id: ../preprints/Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings-September-27-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Integral and fractional expectation thresholds are equivalent" |
| authors: ["OpenAI"] |
| id: ../preprints/Integral-and-fractional-expectation-thresholds-are-equivalent-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Integral points on character varieties of curves" |
| authors: ["OpenAI"] |
| id: ../preprints/Integral-points-on-character-varieties-of-curves-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "Lipschitz Equivalent Separable Banach Spaces Need Not Be Linearly Isomorphic" |
| authors: ["OpenAI"] |
| id: ../preprints/Lipschitz-Equivalent-Separable-Banach-Spaces-Need-Not-Be-Linearly-Isomorphic-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Maximal Seshadri constants on arbitrary polarized surfaces" |
| authors: ["OpenAI"] |
| id: ../preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf |
| type: article |
|
|
| - title: "Memory and precision in noiseless Gaussian regression" |
| authors: ["OpenAI"] |
| id: ../preprints/Memory-and-precision-in-noiseless-Gaussian-regression-September-27-2026/paper.pdf |
| type: article |
|
|
| - title: "Midpoint convexity from bounded tree potentials and path costs" |
| authors: ["OpenAI"] |
| id: ../preprints/Midpoint-convexity-from-bounded-tree-potentials-and-path-costs-September-27-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Midpoint convexity from two recursive potentials" |
| authors: ["OpenAI"] |
| id: ../preprints/Midpoint-convexity-from-two-recursive-potentials-September-27-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Midpoint lenses in segment spaces" |
| authors: ["OpenAI"] |
| id: ../preprints/Midpoint-lenses-in-segment-spaces-September-27-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Nagata's conjecture for plane curves" |
| authors: ["OpenAI"] |
| id: ../preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf |
| type: article |
|
|
| - title: "Near-square-root logarithmic integrality gaps for uniform sparsest cut" |
| authors: ["OpenAI"] |
| id: ../preprints/Near-square-root-logarithmic-integrality-gaps-for-uniform-sparsest-cut-September-24-2026/Near-square-root-logarithmic-integrality-gaps-for-uniform-sparsest-cut-September-24-2026.pdf |
| type: article |
|
|
| - title: "Nontrivial Markov Type Forces Superreflexivity" |
| authors: ["OpenAI"] |
| id: ../preprints/Nontrivial-Markov-Type-Forces-Superreflexivity-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Nonuniqueness for Bounded Measurable Scalar Conductivities in Three Dimensions" |
| authors: ["OpenAI"] |
| id: ../preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Perfect completeness for 2-to-1 games" |
| authors: ["OpenAI"] |
| id: ../preprints/Perfect-completeness-for-2-to-1-games-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Petty’s projection-volume conjecture in dimensions at least four" |
| authors: ["OpenAI"] |
| id: ../preprints/Pettys-projection-volume-conjecture-in-dimensions-at-least-four-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Planar Graph Metrics Embed into $L_1$ with Constant Distortion" |
| authors: ["OpenAI"] |
| id: ../preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Polynomial Hitting Lists for Noncommutative Rational Formulas" |
| authors: ["OpenAI"] |
| id: ../preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026.pdf |
| type: article |
|
|
| - title: "Polynomial removal fails for ordered binary matrices" |
| authors: ["OpenAI"] |
| id: ../preprints/Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "Posterior replicas and conditional information in Gaussian regression" |
| authors: ["OpenAI"] |
| id: ../preprints/Posterior-replicas-and-conditional-information-in-Gaussian-regression-September-27-2026/paper.pdf |
| type: article |
|
|
| - title: "Power-law violations of Yau's nodal upper bound" |
| authors: ["OpenAI"] |
| id: ../preprints/Power-law-violations-of-Yaus-nodal-upper-bound-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Product-projection localization and the QAC⁰ parity lower bound" |
| authors: ["OpenAI"] |
| id: ../preprints/Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Projection moments, positive cap domination, and Riesz estimates on the sphere" |
| authors: ["OpenAI"] |
| id: ../preprints/Projection-moments-positive-cap-domination-and-Riesz-estimates-on-the-sphere-September-27-2026/paper.pdf |
| type: article |
|
|
| - title: "Quadratic stabilization of the canonical Foulkes–Howe map" |
| authors: ["OpenAI"] |
| id: ../preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "Quantitative Superexponential Bounds for van der Waerden Numbers" |
| authors: ["OpenAI"] |
| id: ../preprints/Quantitative-Superexponential-Bounds-for-van-der-Waerden-Numbers-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Randomized quasipolynomial-time mean-payoff games" |
| authors: ["OpenAI"] |
| id: ../preprints/Randomized-quasipolynomial-time-mean-payoff-games-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "Regular trajectories, pruning and quantum parity" |
| authors: ["OpenAI"] |
| id: ../preprints/Regular-trajectories-pruning-and-quantum-parity-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Relative generation and the generator problem for finite factors" |
| authors: ["OpenAI"] |
| id: ../preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Replacing Gaussian observations in memory-constrained inference" |
| authors: ["OpenAI"] |
| id: ../preprints/Replacing-Gaussian-observations-in-memory-constrained-inference-September-27-2026/paper.pdf |
| type: article |
|
|
| - title: "Riesz transforms and uniform rectifiability in higher codimension" |
| authors: ["OpenAI"] |
| id: ../preprints/Riesz-transforms-and-uniform-rectifiability-in-higher-codimension-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Rigidity of the Turing degrees" |
| authors: ["OpenAI"] |
| id: ../preprints/Rigidity-of-the-Turing-degrees-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Routing densities and representation contraction for Thorp sweeps" |
| authors: ["OpenAI"] |
| id: ../preprints/Routing-densities-and-representation-contraction-for-Thorp-sweeps-September-26-2026/paper.pdf |
| type: article |
|
|
| - title: "Sharp binary-information contraction on the discrete cube" |
| authors: ["OpenAI"] |
| id: ../preprints/Sharp-binary-information-contraction-on-the-discrete-cube-September-24-2026/main.pdf |
| type: article |
|
|
| - title: "Sharp one-dimensional Lieb–Thirring constants" |
| authors: ["OpenAI"] |
| id: ../preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Short Egyptian fractions" |
| authors: ["OpenAI"] |
| id: ../preprints/Short-Egyptian-fractions-September-25-2026/Short-Egyptian-fractions-September-25-2026.pdf |
| type: article |
|
|
| - title: "Simulating One-Tape Time in Two-Fifths-Power Space" |
| authors: ["OpenAI"] |
| id: ../preprints/Simulating-One-Tape-Time-in-Two-Fifths-Power-Space-September-25-2026/article.pdf |
| type: article |
|
|
| - title: "Single-exponential recovery and bounded-price strictness for metric k-median" |
| authors: ["OpenAI"] |
| id: ../preprints/Single-Exponential-Recovery-and-Bounded-Price-Strictness-for-Metric-k-Median-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Single-fold Diophantine representations" |
| authors: ["OpenAI"] |
| id: ../preprints/Single-fold-Diophantine-representations-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Smooth counterexamples to Yau's nodal upper bound in dimensions three and four" |
| authors: ["OpenAI"] |
| id: ../preprints/Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Squarefree values of quartics and power-free values of polynomials" |
| authors: ["OpenAI"] |
| id: ../preprints/Squarefree-values-of-quartics-and-power-free-values-of-polynomials-September-24-2026/manuscript.pdf |
| type: article |
|
|
| - title: "Staggered extraction for exact matrix multiplication over every field" |
| authors: ["OpenAI"] |
| id: ../preprints/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026.pdf |
| type: article |
|
|
| - title: "Strict convexity and differentiability of the planar exponential first-passage limit shape" |
| authors: ["OpenAI"] |
| id: ../preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026/main.pdf |
| type: article |
|
|
| - title: "Subpolynomial dimension reduction in $L_p$" |
| authors: ["OpenAI"] |
| id: ../preprints/Subpolynomial-dimension-reduction-in-Lp-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Subpolynomial query complexity for well-conditioned log-concave sampling" |
| authors: ["OpenAI"] |
| id: ../preprints/Subpolynomial-query-complexity-for-well-conditioned-log-concave-sampling-September-26-2026/article.pdf |
| type: article |
|
|
| - title: "Subsphere methods for memory–sample lower bounds in noiseless Gaussian regression" |
| authors: ["OpenAI"] |
| id: ../preprints/Subsphere-methods-for-memory-sample-lower-bounds-in-noiseless-Gaussian-regression-September-27-2026/paper.pdf |
| type: article |
|
|
| - title: "Symmetry of semialgebraic bounded domains with compact quotient" |
| authors: ["OpenAI"] |
| id: ../preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "Symplectic Balls in Symmetric Polar Products" |
| authors: ["OpenAI"] |
| id: ../preprints/Symplectic-Balls-in-Symmetric-Polar-Products-September-22-2026/paper.pdf |
| type: article |
|
|
| - title: "Talagrand's discrete-convexity conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/Talagrands-discrete-convexity-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Taming implies compatibility on four-manifolds" |
| authors: ["OpenAI"] |
| id: ../preprints/Taming-implies-compatibility-on-four-manifolds-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026.pdf |
| type: article |
|
|
| - title: "The circulant Hadamard conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/The-circulant-Hadamard-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The complete Crouzeix theorem: optimal similarity and a common positive boundary representation" |
| authors: ["OpenAI"] |
| id: ../preprints/The-complete-Crouzeix-theorem-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The cotype–cotype conjecture under the approximation property" |
| authors: ["OpenAI"] |
| id: ../preprints/The-cotype-cotype-conjecture-under-the-approximation-property-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The crossing number of complete bipartite graphs" |
| authors: ["OpenAI"] |
| id: ../preprints/The-crossing-number-of-complete-bipartite-graphs-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The crossing number of complete graphs" |
| authors: ["OpenAI"] |
| id: ../preprints/The-crossing-number-of-complete-graphs-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The Deligne-Drinfeld conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Deligne-Drinfeld-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The entropy-rate dimension formula for self-similar measures on the line" |
| authors: ["OpenAI"] |
| id: ../preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/main.pdf |
| type: article |
|
|
| - title: "The Euclidean plane is not five-colorable" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Euclidean-plane-is-not-five-colorable-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The Euclidean Steinitz–Bergström theorem" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Euclidean-Steinitz-Bergstrom-theorem-September-24-2026/The-Euclidean-Steinitz-Bergstrom-theorem-September-24-2026.pdf |
| type: article |
|
|
| - title: "The Factor-Two Hardness Threshold for Vertex Cover" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Factor-Two-Hardness-Threshold-for-Vertex-Cover-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The Falconer distance conjecture in all dimensions" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Falconer-distance-conjecture-in-all-dimensions-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The Gaussian propeller bound in every dimension" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Gaussian-Propeller-Bound-in-Every-Dimension-September-24-2026/main.pdf |
| type: article |
|
|
| - title: "The Grothendieck homotopy hypothesis via elementary expansions" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "The Kirchberg–Rørdam character criterion" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Kirchberg-Rordam-character-criterion-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "The logarithmic Brunn–Minkowski conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/The-logarithmic-Brunn-Minkowski-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The maximal triangular Hilbert transform at the symmetric point" |
| authors: ["OpenAI"] |
| id: ../preprints/The-maximal-triangular-Hilbert-transform-at-the-symmetric-point-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "The Partition Principle does not imply Choice" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Partition-Principle-does-not-imply-Choice-September-24-2026/partition-principle-without-choice.pdf |
| type: article |
|
|
| - title: "The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane Re(s)>7/8" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/paper.pdf |
| type: article |
|
|
| - title: "The second Kahn–Kalai conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/The-second-Kahn-Kalai-conjecture-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "The sharp factor-of-IID threshold for the free Ising model on regular trees" |
| authors: ["OpenAI"] |
| id: ../preprints/The-sharp-factor-of-IID-threshold-for-the-free-Ising-model-on-regular-trees-September-26-2026/article.pdf |
| type: article |
|
|
| - title: "The strong thin tree conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/The-strong-thin-tree-conjecture-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The Subcritical Hénon–Lane–Emden Conjecture" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026/paper.pdf |
| type: article |
|
|
| - title: "The symmetric Mahler conjecture and its equality cases" |
| authors: ["OpenAI"] |
| id: ../preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026/paper.pdf |
| type: article |
|
|
| - title: "The trace cone classifies Razak–Jacelon stabilizations" |
| authors: ["OpenAI"] |
| id: ../preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026.pdf |
| type: article |
|
|
| - title: "The Unique Games Theorem" |
| authors: ["OpenAI"] |
| id: ../preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "The weak pinned planar distance theorem" |
| authors: ["OpenAI"] |
| id: ../preprints/The-weak-pinned-planar-distance-theorem-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Thompson's group F is nonamenable" |
| authors: ["OpenAI"] |
| id: ../preprints/Thompsons-group-F-is-nonamenable-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Three fixed points on the symplectic quadric threefold" |
| authors: ["OpenAI"] |
| id: ../preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Threshold parallel repetition for finite-dimensional entangled games" |
| authors: ["OpenAI"] |
| id: ../preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "Tracial projection methods and uniform property Γ" |
| authors: ["OpenAI"] |
| id: ../preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Two limit cycles for quintic Liénard systems" |
| authors: ["OpenAI"] |
| id: ../preprints/two-limit-cycles-for-quintic-lienard-systems-September-24-2026/two-limit-cycles-for-quintic-lienard-systems-September-24-2026.pdf |
| type: article |
|
|
| - title: "Uniform Bi-Hölder Transport from Weak MTW" |
| authors: ["OpenAI"] |
| id: ../preprints/Uniform-Bi-Holder-Transport-from-Weak-MTW-September-25-2026/paper.pdf |
| type: article |
|
|
| - title: "Uniform Cartier sections for Fano type contractions" |
| authors: ["OpenAI"] |
| id: ../preprints/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026.pdf |
| type: article |
|
|
| - title: "Uniform exclusion of Landau–Siegel zeros" |
| authors: ["OpenAI"] |
| id: ../preprints/Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026/paper.pdf |
| type: article |
|
|
| - title: "Unitarizability implies amenability for discrete groups" |
| authors: ["OpenAI"] |
| id: ../preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Universal-cover splitting for compact Kähler manifolds" |
| authors: ["OpenAI"] |
| id: ../preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf |
| type: article |
|
|
| - title: "Weak Hessian bounds along every geodesic in RCD spaces" |
| authors: ["OpenAI"] |
| id: ../preprints/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026/weak-hessian-geodesics.pdf |
| type: article |
|
|
| related_formalizations: |
| |
| - id: https://github.com/leanprover-community/mathlib4 |
| relationship: builds-on |
|
|
| - id: https://github.com/AlexKontorovich/PrimeNumberTheoremAnd |
| relationship: builds-on |
|
|
| - id: https://github.com/n-yamaguchi-0729/ClassFieldTheory |
| relationship: builds-on |
|
|
| - id: https://github.com/CBirkbeck/AINTLIB |
| relationship: builds-on |
|
|
| - id: https://github.com/math-inc/strongpnt |
| relationship: builds-on |
|
|
| - id: https://github.com/abenenson/rellich-kondrachov |
| relationship: builds-on |
|
|
| - id: https://github.com/harfe/fixed-point-theorems-lean4 |
| relationship: builds-on |
|
|
| - id: https://github.com/TauCetiProject/TauCeti |
| relationship: builds-on |
|
|
| - id: https://github.com/fpvandoorn/carleson |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/heights |
| relationship: builds-on |
|
|
| - id: https://github.com/Aaron1011/gromov |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/iut |
| relationship: builds-on |
|
|
| - id: https://github.com/alonamaloh/schoenflies-lean |
| relationship: builds-on |
|
|
| - id: https://github.com/leanprover-community/sphere-eversion |
| relationship: builds-on |
|
|
| - id: https://github.com/ahhwuhu/zeta_3_irrational |
| relationship: builds-on |
|
|
| - id: https://github.com/BennyAvelin/AbsorptionCutoff |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/belyi |
| relationship: builds-on |
|
|
| - id: https://github.com/PatrickMassot/checkdecls |
| relationship: builds-on |
|
|
| - id: https://github.com/leanprover/doc-gen4 |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/elliptic-curves |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/formal-schemes |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/genl |
| relationship: builds-on |
|
|
| - id: https://github.com/hanwenzhu/LeanArchitect |
| relationship: builds-on |
|
|
| - id: https://github.com/alerad/leancert |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/oka |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/orbicurve-cores |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/pi1 |
| relationship: builds-on |
|
|
| - id: https://github.com/b-mehta/PrimeCert |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/tate-curves-theta |
| relationship: builds-on |
|
|
| - id: https://github.com/lana-agents/tempered-fundamental-groups |
| relationship: builds-on |
|
|
| status: |
| scope: "Partial progress." |
| |
| main_results: |
| - comparator_config: ComparatorChallenges/AbhyankarSathaye.json |
| declaration: OAI.AbhyankarSathaye.exists_noncoordinate_polynomial |
| file: OAI/AlgebraicGeometry/AbhyankarSathaye/Counterexample.lean |
|
|
| - comparator_config: ComparatorChallenges/AmplitudeDamping.json |
| declaration: OAI.GAD.main |
| file: OAI/InformationTheory/AmplitudeDamping/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ArnoldCounterexample.json |
| declaration: OAI.ArnoldCounterexample.main |
| file: OAI/Geometry/Arnold/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ArtinCAT0.json |
| declaration: OAI.ArtinCAT0.main |
| file: OAI/GroupTheory/ArtinCAT0/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/AsymptoticallyMinimalLittlewood.json |
| declaration: OAI.AsymptoticallyMinimalLittlewood.main |
| file: OAI/Analysis/Littlewood/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/AuslanderReiten.json |
| declaration: OAI.ArExplicit.Statement.main |
| file: OAI/Algebra/AuslanderReiten/All.lean |
|
|
| - comparator_config: ComparatorChallenges/BackwardIntertwiners.json |
| declaration: OAI.BackwardIntertwiners.direct_algebra_corollary |
| file: OAI/Analysis/BackwardIntertwiners/AlgebraCorollary.lean |
|
|
| - comparator_config: ComparatorChallenges/BassTrace.json |
| declaration: OAI.BassTrace.RightProjective.bassTraceModules_vanishing_and_support |
| file: OAI/RingTheory/BassTrace/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/BiholderTransport.json |
| declaration: OAI.WeakMTWTransport.uniform_biHolder_transport |
| file: OAI/Analysis/BiholderTransport/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/BinPackingGap.json |
| declaration: OAI.BinPackingGap.main_results |
| file: OAI/Computability/BinPacking/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/BinaryMatching.json |
| declaration: OAI.BinaryMatching.deterministic_approximate_counting |
| file: OAI/Computability/MatchingCount/BinarySolve.lean |
|
|
| - comparator_config: ComparatorChallenges/BinarySweep.json |
| declaration: OAI.binary_sweep_contraction_and_mixing |
| file: OAI/Probability/BinarySweep/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/BipartiteCrossing.json |
| declaration: OAI.Zarankiewicz.mainTarget_proof |
| file: OAI/Combinatorics/Crossing/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/BorsukNine.json |
| declaration: OAI.BorsukNine.main_theorem |
| file: OAI/Geometry/Borsuk/Counterexample.lean |
|
|
| - comparator_config: ComparatorChallenges/BoundedRecovery.json |
| declaration: OAI.BoundedRecovery.bounded_recovery |
| file: OAI/Analysis/ModularRecovery/Recovery.lean |
|
|
| - comparator_config: ComparatorChallenges/BoundedTreePotentials.json |
| declaration: OAI.BoundedTreePotentials.TreeCalculus.main_counterexample |
| file: OAI/Analysis/TreePotential/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/BoundedTreewidthL1.json |
| declaration: OAI.BoundedTreewidthL1.main_theorem |
| file: OAI/Combinatorics/TreewidthL1/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Brennan.json |
| declaration: OAI.Brennan.main_theorem |
| file: OAI/Analysis/IntegralMeans/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/BrennanSharp.json |
| declaration: OAI.Brennan.Sharp.sharp_endpoints |
| file: OAI/Analysis/IntegralMeans/SharpEndpoints.lean |
|
|
| - comparator_config: ComparatorChallenges/C0Absorption.json |
| declaration: OAI.C0Absorption.main_result |
| file: OAI/Analysis/C0Absorption/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CHObstruction.json |
| declaration: OAI.CHObstruction.main |
| file: OAI/ModelTheory/Categoricity/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CartierChartCompactnessSupport.json |
| declaration: OAI.CartierSections.isCompact_closedChartFieldRetraction_cone |
| file: OAI/AlgebraicGeometry/CartierSections/ChartCompactness.lean |
|
|
| - comparator_config: ComparatorChallenges/CharacterCriterion.json |
| declaration: OAI.KirchbergRordam.character_criterion |
| file: OAI/Analysis/CharacterCriterion/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CharacterVarietiesAllSeamsSupport.json |
| declaration: OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.producedMarkedValues_allSeams |
| file: OAI/AlgebraicGeometry/CharacterVarieties/Seams/ProducedSolution.lean |
|
|
| - comparator_config: ComparatorChallenges/ChoicelessPolynomialTime.json |
| declaration: OAI.CPTSeparation.main |
| file: OAI/ModelTheory/Choiceless/Separation.lean |
|
|
| - comparator_config: ComparatorChallenges/CirculantHadamard.json |
| declaration: OAI.CirculantHadamard.exists_iff_order_one_or_four |
| file: OAI/LinearAlgebra/CirculantHadamard/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ClassicalON.json |
| declaration: OAI.ClassicalON.main |
| file: OAI/Probability/ClassicalON/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CliqueFreeLog.json |
| declaration: OAI.CliqueFreeLog.logarithmic_independence_bound |
| file: OAI/Combinatorics/CliqueFree/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CommonBasesFPRAS.json |
| declaration: OAI.common_bases_fpras |
| file: OAI/Combinatorics/MatroidCounting/CommonBases.lean |
|
|
| - comparator_config: ComparatorChallenges/CommutingDerivations.json |
| declaration: OAI.AbhyankarSathaye.CommutingDerivations.commuting_derivations_with_ordinary_extras |
| file: OAI/AlgebraicGeometry/CommutingDerivations/OrdinaryExtraMain.lean |
|
|
| - comparator_config: ComparatorChallenges/CompactBanach.json |
| declaration: OAI.CompactBanach.main |
| file: OAI/Geometry/DoublingHilbert/CompactBanach.lean |
|
|
| - comparator_config: ComparatorChallenges/CompleteCrossing.json |
| declaration: OAI.Paper170.complete_graph_crossing_number |
| file: OAI/Combinatorics/CompleteCrossing/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CompleteCrouzeix.json |
| declaration: OAI.CompleteCrouzeix.main |
| file: OAI/Analysis/NumericalRange/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ComplexCancellation.json |
| declaration: OAI.ComplexCancellation.main |
| file: OAI/Algebra/AffineCancellation/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Conductivity.json |
| declaration: OAI.ScalarConductivity.main_nonuniqueness |
| file: OAI/Analysis/Conductivity/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ConjugatePoints.json |
| declaration: OAI.ThreeManifold.main_theorem |
| file: OAI/Geometry/ConjugatePoints/ThreeManifold.lean |
|
|
| - comparator_config: ComparatorChallenges/ContinuumTransition.json |
| declaration: OAI.ContinuumTemperature.main_theorem |
| file: OAI/Probability/ContinuumTransition/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CoordinateSweeps.json |
| declaration: OAI.CoordinateSweeps.conditional_main |
| file: OAI/Probability/CoordinateSweeps/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Cotype.json |
| declaration: OAI.Cotype.mainTarget_proved |
| file: OAI/Analysis/Cotype/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CoulombIonization.json |
| declaration: OAI.CoulombAtom.generalized_ionization |
| file: OAI/Analysis/CoulombIonization/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CourtadeKumar.json |
| declaration: OAI.LeanBlast.CourtadeKumar.courtadeKumarAndAttainment |
| file: OAI/InformationTheory/BooleanNoise/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CriticalSK.json |
| declaration: OAI.CriticalSK.covariance_and_linear_tests |
| file: OAI/MathematicalPhysics/CriticalSK/Rayleigh.lean |
|
|
| - comparator_config: ComparatorChallenges/CriticalSKMixing.json |
| declaration: OAI.CriticalSK.critical_mixing_bounds |
| file: OAI/MathematicalPhysics/CriticalMixing/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CriticalZ3.json |
| declaration: OAI.CriticalZ3.critical_no_infinite |
| file: OAI/Probability/CriticalZ3/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/CycleDecomposition.json |
| declaration: OAI.ErdosGallai.erdos_gallai |
| file: OAI/Combinatorics/CycleDecomposition/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/DaugavetModuli.json |
| declaration: OAI.ExactModuli.exact_example |
| file: OAI/Analysis/Daugavet/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/DegreeRigidity.json |
| declaration: OAI.TuringRigidity.ManuscriptMain.rigidity |
| file: OAI/Computability/DegreeRigidity/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/DeligneDrinfeld.json |
| declaration: OAI.DeligneDrinfeld.main |
| file: OAI/Algebra/Drinfeld/Completion.lean |
|
|
| - comparator_config: ComparatorChallenges/DepthThree.json |
| declaration: OAI.DepthThreeLowerBound.exists_polynomial_time_language_depth_three_lower_bound |
| file: OAI/Computability/DepthThree/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/DiamondDistortion.json |
| declaration: OAI.DiamondDistortion.headline_all_pairs |
| file: OAI/Analysis/DiamondDistortion/Descent.lean |
|
|
| - comparator_config: ComparatorChallenges/DirectCrouzeix.json |
| declaration: OAI.DirectCrouzeix.complete_crouzeix |
| file: OAI/Analysis/DirectCrouzeix/CompleteBound.lean |
|
|
| - comparator_config: ComparatorChallenges/DirectionalBallisticity.json |
| declaration: OAI.DirectionalTransience.directional_transience_implies_ballisticity |
| file: OAI/Probability/Ballisticity/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/DirichletSevenEighths.json |
| declaration: OAI.DirichletCharacter.LFunction_ne_zero_of_seven_eighths_lt_re |
| file: OAI/NumberTheory/DirichletL/Nonvanishing.lean |
|
|
| - comparator_config: ComparatorChallenges/DixmierAllDiscrete.json |
| declaration: OAI.Dixmier.current_main_theorem |
| file: OAI/Analysis/Unitarizability/AllDiscrete.lean |
|
|
| - comparator_config: ComparatorChallenges/DoublingHilbert.json |
| declaration: OAI.DoublingHilbert.main |
| file: OAI/Geometry/DoublingHilbert/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/EgyptianFractions.json |
| declaration: OAI.Problem337.main_double_log_order |
| file: OAI/NumberTheory/EgyptianFractions/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/EgyptianFractions.json |
| declaration: OAI.Problem337.counting_double_log_order |
| file: OAI/NumberTheory/EgyptianFractions/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/EgyptianFractions.json |
| declaration: OAI.Problem337.prescribed_denominator_corollary |
| file: OAI/NumberTheory/EgyptianFractions/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/EntangledGames.json |
| declaration: OAI.ThresholdParallelRepetition.threshold_parallel_repetition |
| file: OAI/Probability/EntangledGames/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/EuclideanFiveColor.json |
| declaration: OAI.EuclideanFiveColor.no_proper_five_coloring |
| file: OAI/Geometry/PlaneColoring/Five.lean |
|
|
| - comparator_config: ComparatorChallenges/EuclideanRamsey.json |
| declaration: OAI.EuclideanRamsey.classification |
| file: OAI/Combinatorics/EuclideanRamsey/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ExactFourier.json |
| declaration: OAI.ExactFourier.main_theorem |
| file: OAI/Computability/FourierCircuit/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/FactorGeneration.json |
| declaration: OAI.Generator.single_generation_of_II1_separable_predual |
| file: OAI/Analysis/FactorGeneration/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/FinitisticAsymmetry.json |
| declaration: OAI.LittleFinitistic.extreme_left_right_asymmetry |
| file: OAI/Algebra/FinitisticAsymmetry/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ForestSpace.json |
| declaration: OAI.ForestSpace.main_theorem |
| file: OAI/Analysis/ForestSpace/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/FoulkesHowe.json |
| declaration: OAI.Problem346.canonical_foulkes_howe_surjective |
| file: OAI/RepresentationTheory/FoulkesHowe/Stabilization.lean |
|
|
| - comparator_config: ComparatorChallenges/FourierLLogL.json |
| declaration: OAI.FourierLLogL.paperMain |
| file: OAI/Analysis/FourierLLogL/PaperMain.lean |
|
|
| - comparator_config: ComparatorChallenges/FreeIsing.json |
| declaration: OAI.Problem367.free_ising_factor_iff_threshold |
| file: OAI/Probability/FreeIsing/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/GaussianMoat.json |
| declaration: OAI.GaussianMoat.fullMain |
| file: OAI/NumberTheory/GaussianMoat/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/GaussianPropeller.json |
| declaration: OAI.GaussianPropeller.all_partitions |
| file: OAI/Probability/GaussianPropeller/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/GaussianReplacement.json |
| declaration: OAI.CurrentProjection.hybridBlockMain |
| file: OAI/Probability/GaussianReplacement/Hybrid.lean |
|
|
| - comparator_config: ComparatorChallenges/GaussianReplacement.json |
| declaration: OAI.CurrentProjection.fiberBlockMain |
| file: OAI/Probability/GaussianReplacement/FiberBlock.lean |
|
|
| - comparator_config: ComparatorChallenges/GotsmanLinial.json |
| declaration: OAI.LeanBlast.GotsmanLinial.gotsmanLinialStatement |
| file: OAI/Combinatorics/GotsmanLinial/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/GrahamSpherical.json |
| declaration: OAI.GrahamSpherical.full_main |
| file: OAI/Combinatorics/SphericalRamsey/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/GrothendieckElementaryExpansion.json |
| declaration: OAI.Grothendieck.elementary_expansion |
| file: OAI/CategoryTheory/Globular/ElementaryExpansion.lean |
|
|
| - comparator_config: ComparatorChallenges/GroupRingDeterminant.json |
| declaration: OAI.GroupRingDeterminant.main |
| file: OAI/Analysis/GroupDeterminants/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/HadwigerCounterexample.json |
| declaration: OAI.HadwigerCounterexample.not_hadwiger_conjecture |
| file: OAI/Combinatorics/HadwigerCounterexample/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/HarmonicArtin.json |
| declaration: OAI.HarmonicArtin.salvetti_cover_contractible |
| file: OAI/Topology/ArtinGroups/Realizations/SalvettiCoverContractible.lean |
|
|
| - comparator_config: ComparatorChallenges/HarmonicGrowth.json |
| declaration: OAI.HarmonicCounterexample.main |
| file: OAI/Geometry/HarmonicGrowth/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/HeckeSevenEighths.json |
| declaration: OAI.SevenEighths.HeckeFamily.LFunction_ne_zero_of_seven_eighths_lt_re |
| file: OAI/NumberTheory/DirichletL/Hecke/Nonvanishing.lean |
|
|
| - comparator_config: ComparatorChallenges/HenonEmden.json |
| declaration: OAI.HenonLaneEmden.main_nonexistence |
| file: OAI/Analysis/HenonEmden/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/HoneycombBridgeMassSupport.json |
| declaration: OAI.CriticalHoneycomb.finiteBridgeMassEstimate |
| file: OAI/Combinatorics/HoneycombChords/BridgeMass.lean |
|
|
| - comparator_config: ComparatorChallenges/HyperbolicCones.json |
| declaration: OAI.Paper256.main_result |
| file: OAI/Analysis/HyperbolicCones/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/HyperbolicObstruction.json |
| declaration: OAI.HyperbolicObstruction.main |
| file: OAI/Geometry/HyperbolicGroups/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/IndependentProducts.json |
| declaration: OAI.IndependentProducts.main_general |
| file: OAI/Analysis/ProductSpaces/WeakNullity.lean |
|
|
| - comparator_config: ComparatorChallenges/IndependentProducts.json |
| declaration: OAI.IndependentProducts.main_exponential |
| file: OAI/Analysis/ProductSpaces/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/IndependentSets.json |
| declaration: OAI.LargeIndependentSets.mainTheoremReal |
| file: OAI/Combinatorics/IndependentSets/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/InfiniteMatroid.json |
| declaration: OAI.InfiniteMatroidCounterexample.main |
| file: OAI/Combinatorics/InfiniteMatroid/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/IsometricImmersion.json |
| declaration: OAI.SmoothLocal.Geometry.exists_local_metric_without_local_immersion |
| file: OAI/Geometry/IsometricImmersion/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Jacobsthal.json |
| declaration: OAI.Erdos970.Erdos970Final.erdos_970_quadratic |
| file: OAI/NumberTheory/Jacobsthal/Conclusions/QuadraticBound.lean |
|
|
| - comparator_config: ComparatorChallenges/KMedianRecovery.json |
| declaration: OAI.MetricKMedianRecovery.global_application |
| file: OAI/Combinatorics/KMedianRecovery/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/KahlerSplitting.json |
| declaration: OAI.UniversalCoverSplitting.main |
| file: OAI/Geometry/KahlerSplitting/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/KaplanskyFinitelyPresented.json |
| declaration: OAI.KaplanskyCounterexample.finitelyPresented_counterexample |
| file: OAI/RingTheory/DirectFiniteness/FinitelyPresented.lean |
|
|
| - comparator_config: ComparatorChallenges/KaplanskyQuasitrace.json |
| declaration: OAI.Kaplansky.kaplansky_quasitrace_counterexample |
| file: OAI/Analysis/Kaplansky/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Laughlin.json |
| declaration: OAI.Laughlin.mainTarget_proved |
| file: OAI/Analysis/Laughlin/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/LiebThirring.json |
| declaration: OAI.SharpLiebThirring.sharp_lieb_thirring |
| file: OAI/Analysis/LiebThirring/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/LipschitzEquivalence.json |
| declaration: OAI.LipschitzCounterexample.main |
| file: OAI/Analysis/LipschitzEquivalence/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/LittleFinitistic.json |
| declaration: OAI.LittleFinitistic.Main.exists_counterexample |
| file: OAI/Algebra/Finitistic/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/LogBrunnMinkowski.json |
| declaration: OAI.LogBrunnMinkowski.main |
| file: OAI/Geometry/LogVolume/BrunnMinkowski.lean |
|
|
| - comparator_config: ComparatorChallenges/LogConcaveQuery.json |
| declaration: OAI.LogConcaveSampling.exact_source_main |
| file: OAI/Probability/LogConcave/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/LogspaceEquality.json |
| declaration: OAI.ExactDerandomization.exact_logarithmic_space_derandomization |
| file: OAI/Computability/Logspace/Equality.lean |
|
|
| - comparator_config: ComparatorChallenges/MahlerConjecture.json |
| declaration: OAI.SymmetricMahler.symmetric_mahler |
| file: OAI/Analysis/Mahler/MainTheorem.lean |
|
|
| - comparator_config: ComparatorChallenges/MarkovType.json |
| declaration: OAI.MarkovSuperreflexivity.hasNontrivialMarkovType_iff_hasEquivalentUCNorm |
| file: OAI/Analysis/MarkovType/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MatchingEntropy.json |
| declaration: OAI.MatchingEntropy.entropy_main |
| file: OAI/Combinatorics/PerfectMatching/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MatrixFields.json |
| declaration: OAI.MatrixAllFields.MatrixMultiplication.AllFieldMain.omega_lt_source_constant |
| file: OAI/LinearAlgebra/MatrixFields/Conclusions/AllFieldsBound.lean |
|
|
| - comparator_config: ComparatorChallenges/MatrixMultiplication.json |
| declaration: OAI.MatrixMultiplication.complex_omega_le_nine_quarters |
| file: OAI/LinearAlgebra/MatrixMultiplication/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MatrixMultiplication.json |
| declaration: OAI.MatrixMultiplication.complex_alpha_gt_93_div_200 |
| file: OAI/LinearAlgebra/MatrixMultiplication/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MatrixMultiplication.json |
| declaration: OAI.MatrixMultiplication.complex_rectangular_omega_lt_523_div_250 |
| file: OAI/LinearAlgebra/MatrixMultiplication/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MatrixRemoval.json |
| declaration: OAI.Problem348.no_polynomial_removal_bound |
| file: OAI/Combinatorics/MatrixRemoval/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MaximalSeshadriConstants.json |
| declaration: OAI.MaximalSeshadri.Geometry.maximalSeshadriConstants |
| file: OAI/AlgebraicGeometry/Seshadri/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MemoryPrecision.json |
| declaration: OAI.MemoryPrecision.main |
| file: OAI/Probability/MemoryPrecision/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MetricEntropyDuality.json |
| declaration: OAI.MetricEntropyDuality.exists_entropy_duality_counterexample_with_covers |
| file: OAI/Analysis/MetricEntropy/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/MidpointLenses.json |
| declaration: OAI.SegmentLenses.midpoint_lens_main |
| file: OAI/Analysis/SegmentLenses/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Nagata.json |
| declaration: OAI.Nagata.nagata_conjecture |
| file: OAI/AlgebraicGeometry/PlaneCurves/Nagata.lean |
|
|
| - comparator_config: ComparatorChallenges/OddKaplansky.json |
| declaration: OAI.OddKaplansky.main_theorem |
| file: OAI/Algebra/OddKaplansky/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/OneTapeSpace.json |
| declaration: OAI.Fifths.Single.capped |
| file: OAI/Computability/SpaceSimulation/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/OneTapeSpace.json |
| declaration: OAI.Fifths.Single.unknown |
| file: OAI/Computability/SpaceSimulation/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/OneWayLiveness.json |
| declaration: OAI.OneWayLiveness.main_theorem |
| file: OAI/Combinatorics/Automata/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/OptimalMaxCut.json |
| declaration: OAI.OptimalMaxCut.main |
| file: OAI/Computability/MaxCut/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/PartitionPrinciple.json |
| declaration: OAI.PartitionPilot.Forcing.TransitiveGround.exists_model_partitionPrinciple_without_choice |
| file: OAI/SetTheory/PartitionPrinciple/Models/Separation.lean |
|
|
| - comparator_config: ComparatorChallenges/PerfectCompleteness.json |
| declaration: OAI.PerfectCompleteness.Theorem11.exists_reduction |
| file: OAI/Computability/PerfectCompleteness/Theorem11.lean |
|
|
| - comparator_config: ComparatorChallenges/PeriodicTilingThree.json |
| declaration: OAI.PeriodicTilingThree.periodic_tiling_counterexample_and_minimality |
| file: OAI/Geometry/PeriodicTiling/Counterexample.lean |
|
|
| - comparator_config: ComparatorChallenges/PettyProjectionVolume.json |
| declaration: OAI.PettyProjection.petty_projection_volume |
| file: OAI/Geometry/ProjectionBodies/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/PinchedKahler.json |
| declaration: OAI.PinchedHartogs.main_theorem |
| file: OAI/Geometry/Kahler/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/PinnedDistances.json |
| declaration: OAI.WeakPinned.main |
| file: OAI/Geometry/PinnedDistances/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/PlanarFalconer.json |
| declaration: OAI.PlanarFalconer.mainTarget_proved |
| file: OAI/MeasureTheory/Falconer/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/PlanarFirstPassage.json |
| declaration: OAI.PlanarFPP.manuscriptMain |
| file: OAI/Probability/FirstPassage/BoundaryCurve.lean |
|
|
| - comparator_config: ComparatorChallenges/PlanarL1.json |
| declaration: OAI.PlanarL1.planar_graph_metrics_embed_L1 |
| file: OAI/Combinatorics/PlanarL1/Embedding.lean |
|
|
| - comparator_config: ComparatorChallenges/PlaneColoring.json |
| declaration: OAI.Problem160.properColoring_seven |
| file: OAI/Geometry/PlaneColoring/Seven.lean |
|
|
| - comparator_config: ComparatorChallenges/PosteriorReplicas.json |
| declaration: OAI.PosteriorReplicas.source_main |
| file: OAI/Probability/PosteriorReplicas/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/PowerFreeValues.json |
| declaration: OAI.QuarticPowerFree.allDegrees |
| file: OAI/NumberTheory/PowerFree/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ProjectionCounterexample.json |
| declaration: OAI.ProjectionCounterexample.universal_simplex_upper_bound_false |
| file: OAI/Geometry/ProjectionBody/Counterexample.lean |
|
|
| - comparator_config: ComparatorChallenges/ProjectionMoments.json |
| declaration: OAI.ProjectionMoments.main |
| file: OAI/Probability/ProjectionMoments/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ProjectionVolume.json |
| declaration: OAI.Paper092.product_counterexample |
| file: OAI/Geometry/ProjectionVolume/ProductCounterexample.lean |
|
|
| - comparator_config: ComparatorChallenges/QACParity.json |
| declaration: OAI.QAC.parity_lower_bound |
| file: OAI/InformationTheory/QuantumCircuit/Parity.lean |
|
|
| - comparator_config: ComparatorChallenges/QuadricBundles.json |
| declaration: OAI.QuadricCounterexample.main_theorem |
| file: OAI/Geometry/QuadricBundles/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/QuantitativeVanDerWaerden.json |
| declaration: OAI.QuantitativeVanDerWaerden.uniform_lower_bound |
| file: OAI/Combinatorics/ProgressionColoring/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/QuasiRiemannHypothesis.json |
| declaration: OAI.riemannZeta_ne_zero_of_seven_eighths_lt_re |
| file: OAI/NumberTheory/DirichletL/Nonvanishing.lean |
|
|
| - comparator_config: ComparatorChallenges/QuinticLienard.json |
| declaration: OAI.QuinticLienard.main |
| file: OAI/Analysis/LienardCycles/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/RadialTransition.json |
| declaration: OAI.RadialTransition.main |
| file: OAI/Probability/RadialTransition/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/RandomizedMeanPayoff.json |
| declaration: OAI.randomized_quasipolynomial_mean_payoff |
| file: OAI/Computability/RandomMean/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/RationalHitting.json |
| declaration: OAI.RationalHitting.main |
| file: OAI/Computability/RationalHitting/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/RecursivePotentials.json |
| declaration: OAI.ComparatorModel.RecursivePotentials.main |
| file: OAI/Analysis/RecursivePotentials/Challenge.lean |
|
|
| - comparator_config: ComparatorChallenges/ReflexiveFixedPoints.json |
| declaration: OAI.ReflexiveFixedPoints.exists_fixedPoint_of_canonicallyReflexive |
| file: OAI/Analysis/Nonexpansive/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/RegularParity.json |
| declaration: OAI.QAC.parity_lower_bound_polynomial_size |
| file: OAI/InformationTheory/QuantumCircuit/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/RieszQuantitative.json |
| declaration: OAI.RieszRectifiability.quantitative_higher_codimension_riesz_rectifiability |
| file: OAI/Analysis/RieszRectifiability/Uniformity/Rectifiability.lean |
|
|
| - comparator_config: ComparatorChallenges/RyserCovering.json |
| declaration: OAI.RyserCoveringCounterexample.exists_prime_eventually_counterexampleRank |
| file: OAI/Combinatorics/Ryser/Construction/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/RyserOddExtensions.json |
| declaration: OAI.RyserOdd.eventualOddFailures_and_infinite |
| file: OAI/Combinatorics/Ryser/OddExtensions.lean |
|
|
| - comparator_config: ComparatorChallenges/Saxl.json |
| declaration: OAI.Saxl.saxl_conjecture |
| file: OAI/RepresentationTheory/Saxl/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SecondKahnKalai.json |
| declaration: OAI.LeanBlast.SecondKahnKalai.secondKahnKalaiBounds |
| file: OAI/Combinatorics/GraphThreshold/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SelfSimilar.json |
| declaration: OAI.EntropyRateDimension.entropy_rate_dimension |
| file: OAI/MeasureTheory/SelfSimilar/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SensitivitySeparation.json |
| declaration: OAI.Paper320.quantitative_separation |
| file: OAI/Combinatorics/Sensitivity/Separation.lean |
|
|
| - comparator_config: ComparatorChallenges/SeymourSecondNeighborhood.json |
| declaration: OAI.SeymourSecondNeighborhood.exists_goodVertex |
| file: OAI/Combinatorics/SecondNeighborhood/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SiegelZeros.json |
| declaration: OAI.SiegelZeros.WeightedTorusJets.exists_absolute_real_zero_gap |
| file: OAI/NumberTheory/SiegelZeros/Conclusions/Theorem.lean |
|
|
| - comparator_config: ComparatorChallenges/SignedFiniteBand.json |
| declaration: OAI.SignedDisk.CenteredDiskEndpoint.main_signed_finite_band |
| file: OAI/Analysis/SignedDisk/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SimpleAmenable.json |
| declaration: OAI.SimpleAmenable.main |
| file: OAI/GroupTheory/SimpleAmenable/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SingleFold.json |
| declaration: OAI.SingleFold.main |
| file: OAI/NumberTheory/SingleFold/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SingleLatticeCovering.json |
| declaration: OAI.SingleLatticeCovering.single_lattice_covering |
| file: OAI/Geometry/LatticeCovering/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SingletonLoopMatching.json |
| declaration: OAI.LoopMatching.fullEndpoint |
| file: OAI/Computability/LoopMatching/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SmoothYau.json |
| declaration: OAI.YauCounterexamples.sphere_three |
| file: OAI/Geometry/SmoothYau/SphereMetric/ThreeSphere.lean |
|
|
| - comparator_config: ComparatorChallenges/SmoothYau.json |
| declaration: OAI.YauCounterexamples.sphere_two_torus_two |
| file: OAI/Geometry/SmoothYau/ProductMetric/SphereProduct.lean |
|
|
| - comparator_config: ComparatorChallenges/StableCoordinateFour.json |
| declaration: OAI.StableCoordinate.principal_package |
| file: OAI/AlgebraicGeometry/StableCoordinate/Principal.lean |
|
|
| - comparator_config: ComparatorChallenges/SteinitzBergstrom.json |
| declaration: OAI.EuclideanSteinitzBergstrom.main |
| file: OAI/Analysis/Steinitz/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/StrictMeans.json |
| declaration: OAI.StrictInverseFirstPower.main |
| file: OAI/Analysis/StrictMeans/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/StrongThinTree.json |
| declaration: OAI.StrongThinTree.strongThinTree |
| file: OAI/Combinatorics/ThinTrees/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/StructuralCrouzeix.json |
| declaration: OAI.StructuralCrouzeixReference.challenge |
| file: OAI/Analysis/StructuralCrouzeix/Endpoint.lean |
|
|
| - comparator_config: ComparatorChallenges/SubpolynomialLp.json |
| declaration: OAI.SubpolynomialLp.source_main |
| file: OAI/Analysis/LpDimension/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SubsphereCurrent.json |
| declaration: OAI.SubsphereCurrent.full_current_main_scope |
| file: OAI/Probability/Subsphere/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Superstring.json |
| declaration: OAI.Superstring.main |
| file: OAI/Computability/Superstring/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SurfaceConeCandidateSupport.json |
| declaration: OAI.SmallCM.candidate_ring_properties |
| file: OAI/AlgebraicGeometry/SurfaceCones/CandidateRing.lean |
|
|
| - comparator_config: ComparatorChallenges/SymmetricDomains.json |
| declaration: OAI.Release061.main |
| file: OAI/Analysis/SymmetricDomains/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/SymmetricMahlerEquality.json |
| declaration: OAI.SymmetricMahler.symmetric_mahler_equality |
| file: OAI/Analysis/Mahler/Classification.lean |
|
|
| - comparator_config: ComparatorChallenges/SymmetricPolar.json |
| declaration: OAI.SymmetricPolar.symmetric_polar_main |
| file: OAI/Geometry/PolarProducts/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/Tachikawa.json |
| declaration: OAI.Tachikawa.main_theorem |
| file: OAI/RingTheory/Tachikawa/Counterexample.lean |
|
|
| - comparator_config: ComparatorChallenges/TalagrandDiscreteConvexity.json |
| declaration: OAI.TalagrandDiscreteConvexity.talagrand_discrete_convexity |
| file: OAI/Combinatorics/DiscreteConvexity/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/TalagrandExpectationThreshold.json |
| declaration: OAI.TalagrandThreshold.talagrand_expectation_threshold_equivalence |
| file: OAI/Combinatorics/ExpectationThreshold/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/TamingCompatibility.json |
| declaration: OAI.TamingCompatibility.taming_implies_compatibility |
| file: OAI/Geometry/TamingCompatibility/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ThompsonNonamenability.json |
| declaration: OAI.ThompsonNonamenability.thompson_F_nonamenable_composition |
| file: OAI/GroupTheory/Thompson/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ThorpRouting.json |
| declaration: OAI.ThorpNine.main |
| file: OAI/Probability/ThorpRouting/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/ThorpWeightedCompatibility.json |
| declaration: OAI.ThorpCompatibility.weightedCompatibility_main |
| file: OAI/Probability/ThorpCompatibility/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/TingleySphereIsometry.json |
| declaration: OAI.Tingley.tingley_sphere_isometry_full |
| file: OAI/Analysis/SphereIsometry/Extension.lean |
|
|
| - comparator_config: ComparatorChallenges/TorsionFreeHyperbolic.json |
| declaration: OAI.Release075.main |
| file: OAI/GroupTheory/Hyperbolic/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/TorsionFreeZeroDivisors.json |
| declaration: OAI.TorsionFreeZeroDivisors.main |
| file: OAI/Algebra/GroupRing/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/TraceIdealTransportSupport.json |
| declaration: OAI.TraceConeClassification.TraceConeEquiv.idealOrderIso_finIdeal |
| file: OAI/Analysis/TraceCone/IdealTransport.lean |
|
|
| - comparator_config: ComparatorChallenges/TraceIdealTransportSupport.json |
| declaration: OAI.TraceConeClassification.TraceConeEquiv.idealOrderIso_zeroIdeal |
| file: OAI/Analysis/TraceCone/IdealTransport.lean |
|
|
| - comparator_config: ComparatorChallenges/TraceIdealTransportSupport.json |
| declaration: OAI.TraceConeClassification.closed_ideal_weight_exists |
| file: OAI/Analysis/TraceCone/FiniteIdeal.lean |
|
|
| - comparator_config: ComparatorChallenges/TriangularHilbert.json |
| declaration: OAI.TriangularHilbert.main_estimate |
| file: OAI/Analysis/TriangularHilbert/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/TwoWayComplementation.json |
| declaration: OAI.TwoWayComplementation.complementation_lower_bound_finite |
| file: OAI/Combinatorics/TwoWayAutomata/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/TwoWayDeterminization.json |
| declaration: OAI.TwoWayComplementation.explicit_family_main |
| file: OAI/Combinatorics/TwoWayAutomata/ExplicitFamily.lean |
|
|
| - comparator_config: ComparatorChallenges/UniformFourier.json |
| declaration: OAI.PowerSaving.transform_main |
| file: OAI/Computability/FourierTransform/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/UniformFourier.json |
| declaration: OAI.PowerSaving.convolution_main |
| file: OAI/Computability/FourierTransform/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/UniformGamma.json |
| declaration: OAI.ComparatorModel.CurrentMain.main |
| file: OAI/Analysis/TracialSplitting/Challenge.lean |
|
|
| - comparator_config: ComparatorChallenges/UniformSparsestCut.json |
| declaration: OAI.UniformSparsestCut.mainGap |
| file: OAI/Combinatorics/SparsestCut/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/UniqueGamesTheorem.json |
| declaration: OAI.UniqueGamesTheorem.theorem11 |
| file: OAI/Computability/UniqueGames/Theorem.lean |
|
|
| - comparator_config: ComparatorChallenges/UniversalFInfinity.json |
| declaration: OAI.UniversalFInfinity.universal_group_of_type_FInfinity |
| file: OAI/GroupTheory/UniversalGroup/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/VertexCover.json |
| declaration: OAI.VertexCover.every_fixed_factor_below_two |
| file: OAI/Computability/VertexCover/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/VlasovMaxwell.json |
| declaration: OAI.RVM.global_classical_solution |
| file: OAI/Analysis/VlasovMaxwell/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/WeakHessian.json |
| declaration: OAI.WeakHessian.every_geodesic |
| file: OAI/Geometry/WeakHessian/Main.lean |
|
|
| - comparator_config: ComparatorChallenges/WeakMTWGlobalSupport.json |
| declaration: OAI.WeakMTWGlobalSupport.current_main_convexity |
| file: OAI/Geometry/WeakMTW/Convexity.lean |
|
|
| - comparator_config: ComparatorChallenges/YauCounterexample.json |
| declaration: OAI.Yau.Target.yau_nodal_set_upper_bound_counterexample |
| file: OAI/Geometry/NodalSets/Main.lean |
|
|
| automation: |
| methods: |
| - method: agent |
|
|
| review: |
| status: unchecked |
|
|
| acknowledgements: >- |
| Thank you very much to the authors of Lean 4, mathlib, and the other imported |
| libraries listed above, as well as to the authors of Lake, Comparator, |
| lean4export, and related tools. |
| |
