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OpenAI just dropped 700 preprints of mathematical proofs and counterexamples

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Name	Name	Last commit message	Last commit date
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A-C1-Counterexample-to-the-Entropy-Conjecture-September-25-2026	A-C1-Counterexample-to-the-Entropy-Conjecture-September-25-2026
A-CH-Obstruction-to-a-Prescribed-Categoricity-Threshold-September-24-2026	A-CH-Obstruction-to-a-Prescribed-Categoricity-Threshold-September-24-2026
A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees-October-5-2026	A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees-October-5-2026
A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026	A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026
A-Codimension-One-Bound-for-the-Singular-Set-of-a-Stationary-Integral-Varifold-October-5-2026	A-Codimension-One-Bound-for-the-Singular-Set-of-a-Stationary-Integral-Varifold-October-5-2026
A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026	A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026
A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026	A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026
A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026	A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026
A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026	A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026
A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026	A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026
A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026	A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026
A-Counterexample-to-Rysers-Covering-Conjecture-September-23-2026	A-Counterexample-to-Rysers-Covering-Conjecture-September-23-2026
A-Counterexample-to-Walls-D2-Problem-October-6-2026	A-Counterexample-to-Walls-D2-Problem-October-6-2026
A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026	A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026
A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026	A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026
A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026	A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026
A-Direct-Proof-of-Optimal-Max-Cut-Hardness-September-23-2026	A-Direct-Proof-of-Optimal-Max-Cut-Hardness-September-23-2026
A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026	A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026
A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026	A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026
A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026	A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026
A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026	A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026
A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026	A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026
A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026	A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026
A-Logarithmic-Independence-Bound-for-Clique-Free-Graphs-September-25-2026	A-Logarithmic-Independence-Bound-for-Clique-Free-Graphs-September-25-2026
A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026	A-Low-Space-Algorithm-for-Worst-Case-Subset-Sum-September-26-2026
A-Modulus-Proof-of-Cannons-Conjecture-September-23-2026	A-Modulus-Proof-of-Cannons-Conjecture-September-23-2026
A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026	A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026
A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026	A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026
A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026	A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026
A-PD4-group-without-an-aspherical-manifold-model-September-24-2026	A-PD4-group-without-an-aspherical-manifold-model-September-24-2026
A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula-October-5-2026	A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula-October-5-2026
A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026	A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026
A-Power-Saving-for-Polynomial-Differences-at-Prime-Arguments-October-5-2026	A-Power-Saving-for-Polynomial-Differences-at-Prime-Arguments-October-5-2026
A-Sharp-Threshold-Bound-for-Monotone-Graph-Properties-September-25-2026	A-Sharp-Threshold-Bound-for-Monotone-Graph-Properties-September-25-2026
A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026	A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026
A-Three-Dimensional-Counterexample-to-Integer-Degree-Harmonic-Dimension-Comparison-September-26-2026	A-Three-Dimensional-Counterexample-to-Integer-Degree-Harmonic-Dimension-Comparison-September-26-2026
A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026	A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026
A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026	A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026
A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026	A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026
A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026	A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026
A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026	A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026
A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026	A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026
A-boundary-only-obstruction-to-four-dimensional-disk-embedding-September-24-2026	A-boundary-only-obstruction-to-four-dimensional-disk-embedding-September-24-2026
A-classification-of-finite-Euclidean-Ramsey-configurations-September-23-2026	A-classification-of-finite-Euclidean-Ramsey-configurations-September-23-2026
A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026	A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026
A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026	A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026
A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026	A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026
A-counterexample-to-Hadwigers-conjecture-September-23-2026	A-counterexample-to-Hadwigers-conjecture-September-23-2026
A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026	A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026
A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026	A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026
A-counterexample-to-Sidorenkos-conjecture-September-23-2026	A-counterexample-to-Sidorenkos-conjecture-September-23-2026
A-counterexample-to-Tachikawas-second-conjecture-September-23-2026	A-counterexample-to-Tachikawas-second-conjecture-September-23-2026
A-counterexample-to-integer-degree-harmonic-dimension-comparison-September-25-2026	A-counterexample-to-integer-degree-harmonic-dimension-comparison-September-25-2026
A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026	A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026
A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026	A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026
A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026	A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026
A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026	A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026
A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026	A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026
A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026	A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026
A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026	A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026
A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026	A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026
A-direct-proof-of-the-complete-Crouzeix-inequality-September-26-2026	A-direct-proof-of-the-complete-Crouzeix-inequality-September-26-2026
A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026	A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026
A-directional-zero-one-law-under-strict-ellipticity-September-23-2026	A-directional-zero-one-law-under-strict-ellipticity-September-23-2026
A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026	A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026
A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026	A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026
A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026	A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026
A-finite-entropy-system-without-a-smooth-positive-volume-model-September-25-2026	A-finite-entropy-system-without-a-smooth-positive-volume-model-September-25-2026
A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026	A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026
A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026	A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026
A-group-without-fixed-price-October-5-2026	A-group-without-fixed-price-October-5-2026
A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026	A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026
A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026	A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026
A-latest-anchor-induction-with-spectrally-compact-masks-for-worst-case-trace-reconstruction-October-5-2026	A-latest-anchor-induction-with-spectrally-compact-masks-for-worst-case-trace-reconstruction-October-5-2026
A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026	A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026
A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026	A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026
A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026	A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026
A-marked-tensor-obstruction-to-four-dimensional-disk-embedding-September-24-2026	A-marked-tensor-obstruction-to-four-dimensional-disk-embedding-September-24-2026
A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026	A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026
A-nine-dimensional-counterexample-to-Borsuks-covering-assertion-September-23-2026	A-nine-dimensional-counterexample-to-Borsuks-covering-assertion-September-23-2026
A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026	A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026
A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-September-24-2026	A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-September-24-2026
A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026	A-polynomial-time-algorithm-for-three-machine-unit-job-scheduling-September-24-2026
A-polynomial-time-construction-of-strong-thin-trees-September-23-2026	A-polynomial-time-construction-of-strong-thin-trees-September-23-2026
A-positive-solution-to-Tingleys-problem-September-23-2026	A-positive-solution-to-Tingleys-problem-September-23-2026
A-power-improvement-in-the-Heilbronn-triangle-lower-bound-September-25-2026	A-power-improvement-in-the-Heilbronn-triangle-lower-bound-September-25-2026
A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026	A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026
A-power-saving-for-planar-halving-lines-September-25-2026	A-power-saving-for-planar-halving-lines-September-25-2026
A-power-saving-for-planar-unit-distances-September-23-2026	A-power-saving-for-planar-unit-distances-September-23-2026
A-power-saving-for-square-difference-free-sets-September-24-2026	A-power-saving-for-square-difference-free-sets-September-24-2026
A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026	A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026
A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026	A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026
A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026	A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026
A-quadratic-bound-for-Jacobsthals-function-September-25-2026	A-quadratic-bound-for-Jacobsthals-function-September-25-2026
A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026	A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026
A-rational-obstruction-to-strong-chromatic-splitting-at-height-three-September-25-2026	A-rational-obstruction-to-strong-chromatic-splitting-at-height-three-September-25-2026
A-sharp-Fourier-certificate-for-planar-circle-packing-September-23-2026	A-sharp-Fourier-certificate-for-planar-circle-packing-September-23-2026
A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants-October-5-2026	A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants-October-5-2026
A-single-lattice-covering-bound-of-order-n-log-n-September-23-2026	A-single-lattice-covering-bound-of-order-n-log-n-September-23-2026
A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026	A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026