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• 0 votes 0 replies 20 views Discussion A Lean proof of Theorem 1.2 in OpenAI's local smoothing paper Using Yui, a formalization harness I developed, I completed an unconditional Lean formalization of Theorem 1.2 (critical annular estimate) in OpenAI's paper Local smoothing for the Euclidean wave equation. The… lean-formalizedopenai-math Kaiwen Jin 1 · 12 hours ago

Discussion A Lean proof of Theorem 1.2 in OpenAI's local smoothing paper

Using Yui, a formalization harness I developed, I completed an unconditional Lean formalization of Theorem 1.2 (critical annular estimate) in OpenAI's paper Local smoothing for the Euclidean wave equation. The…

• 0 votes 1 reply 141 views Paper Hilbert’s tenth problem over ℚ Proves that no algorithm decides whether an integer-coefficient polynomial in an arbitrary number of variables has a rational zero, resolving Hilbert's tenth problem over ℚ negatively. Manuscripts (2) Hilbert’s tenth… math.NT openai-math openai/math import · Oct 7

Paper Hilbert’s tenth problem over ℚ

Proves that no algorithm decides whether an integer-coefficient polynomial in an arbitrary number of variables has a rational zero, resolving Hilbert's tenth problem over ℚ negatively. Manuscripts (2) Hilbert’s tenth…

• 0 votes 1 reply 31 views Paper Sharp Cartan–Hadamard isoperimetry and rigidity Proves generalized Cartan–Hadamard isoperimetry in every dimension: in a complete simply connected manifold with sectional curvature at most κ ≤ 0, every finite-volume finite-perimeter set satisfies the sharp comparison… math.DG openai-math openai/math import · Sep 23

Paper Sharp Cartan–Hadamard isoperimetry and rigidity

Proves generalized Cartan–Hadamard isoperimetry in every dimension: in a complete simply connected manifold with sectional curvature at most κ ≤ 0, every finite-volume finite-perimeter set satisfies the sharp comparison…

• 0 votes 1 reply 43 views Paper The Falconer distance conjecture Resolves the Falconer distance conjecture in every dimension d ≥ 2: every compact set E\subset\mathbb R^d with Hausdorff dimension greater than d/2 determines a set of Euclidean distances of positive Lebesgue… math.CA lean-formalizedopenai-math openai/math import · Sep 23

Paper The Falconer distance conjecture

Resolves the Falconer distance conjecture in every dimension d ≥ 2: every compact set E\subset\mathbb R^d with Hausdorff dimension greater than d/2 determines a set of Euclidean distances of positive Lebesgue…

• 0 votes 1 reply 87 views Paper Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity Using logarithmic Iitaka subadditivity, proves log abundance in every dimension for normal compact Kähler log canonical pairs with effective rational boundary: an analytically nef ℚ-Cartier adjoint is semiample. It also… math.AG openai-math openai/math import · Oct 6

Paper Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity

Using logarithmic Iitaka subadditivity, proves log abundance in every dimension for normal compact Kähler log canonical pairs with effective rational boundary: an analytically nef ℚ-Cartier adjoint is semiample. It also…

• 0 votes 1 reply 72 views Paper Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan Proves the restricted geometric Langlands equivalence for connected reductive groups on smooth projective connected curves over \overline{\mathbb F}_q under the four stated Lie-theoretic characteristic hypotheses. Over… math.NT openai-math openai/math import · Oct 5

Paper Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan

Proves the restricted geometric Langlands equivalence for connected reductive groups on smooth projective connected curves over \overline{\mathbb F}_q under the four stated Lie-theoretic characteristic hypotheses. Over…

• 0 votes 1 reply 86 views Paper Projective contact classification and the LeBrun–Salamon conjecture Proves the LeBrun–Salamon conjecture: every closed connected positive quaternionic-Kähler manifold of real dimension at least eight is homothetic to a compact symmetric Wolf space. It also proves contact-Fano homogeneity… math.AG openai-math openai/math import · Sep 23

Paper Projective contact classification and the LeBrun–Salamon conjecture

Proves the LeBrun–Salamon conjecture: every closed connected positive quaternionic-Kähler manifold of real dimension at least eight is homothetic to a compact symmetric Wolf space. It also proves contact-Fano homogeneity…

• 0 votes 0 replies 132 views Paper On the generic case of Jiang's conjecture Chi-Heng Lo (2026) Jiang's conjecture predicts that if π is a generic representation of a quasi-split p-adic group, then the L-parameter of the Aubert-Zelevinsky involution of π must be trivial on… math.RT MA JIAJUN 1 · 11 days ago

Paper On the generic case of Jiang's conjecture

Chi-Heng Lo (2026) Jiang's conjecture predicts that if π is a generic representation of a quasi-split p-adic group, then the L-parameter of the Aubert-Zelevinsky involution of π must be trivial on…

• 0 votes 1 reply 101 views Paper Nagata’s conjecture and maximal Seshadri constants Proves Nagata's strict inequality \sum_i m_i\lt d\sqrt r for every nonzero effective plane curve of degree d through r ≥ 10 very general complex points, with arbitrary multiplicities mi. It also proves maximal… math.AG lean-formalizedopenai-math openai/math import · Oct 5

Paper Nagata’s conjecture and maximal Seshadri constants

Proves Nagata's strict inequality \sum_i m_i\lt d\sqrt r for every nonzero effective plane curve of degree d through r ≥ 10 very general complex points, with arbitrary multiplicities mi. It also proves maximal…

• 0 votes 1 reply 260 views Paper The quasi-Riemann hypothesis Proves that every Dirichlet L-function, including \zeta(s), is zero-free in \Re s\gt 7/8, resolving the quasi-Riemann hypothesis. The same half-plane is zero-free for every finite-order Hecke L-function over… math.NT lean-formalizedopenai-math openai/math import · Oct 5

Paper The quasi-Riemann hypothesis

Proves that every Dirichlet L-function, including \zeta(s), is zero-free in \Re s\gt 7/8, resolving the quasi-Riemann hypothesis. The same half-plane is zero-free for every finite-order Hecke L-function over…

• 0 votes 1 reply 242 views Paper A counterexample to the nearby Lagrangian conjecture Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even N, constructs a closed exact embedded Lagrangian in T^*(S^9\times S^{N-1}) that is diffeomorphic to the base but not Hamiltonian… math.DG openai-math openai/math import · Sep 23

Paper A counterexample to the nearby Lagrangian conjecture

Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even N, constructs a closed exact embedded Lagrangian in T^*(S^9\times S^{N-1}) that is diffeomorphic to the base but not Hamiltonian…

• 0 votes 1 reply 84 views Paper Brennan's conjecture and the integral-means spectrum Proves Brennan's conjecture: for every conformal bijection ϕ from a simply connected plane domain onto the disk, |\phi'|^s is area-integrable for 4/3\lt s\lt 4. The sharp universal integral-means identity is… math.CA lean-formalizedopenai-math openai/math import · Sep 24

Paper Brennan's conjecture and the integral-means spectrum

Proves Brennan's conjecture: for every conformal bijection ϕ from a simply connected plane domain onto the disk, |\phi'|^s is area-integrable for 4/3\lt s\lt 4. The sharp universal integral-means identity is…

• 0 votes 1 reply 99 views Paper Cannon's conjecture Every word-hyperbolic group with boundary homeomorphic to S2 admits a proper cocompact isometric action on hyperbolic three-space with finite kernel, proving Cannon's conjecture. Every torsion-free such group is… math.GR openai-math openai/math import · Sep 23

Paper Cannon's conjecture

Every word-hyperbolic group with boundary homeomorphic to S2 admits a proper cocompact isometric action on hyperbolic three-space with finite kernel, proving Cannon's conjecture. Every torsion-free such group is…

• 0 votes 2 replies 482 views Paper Local smoothing for the Euclidean wave equation Proves Sogge’s local smoothing conjecture in every spatial dimension n\ge2, with arbitrarily small loss above the sharp Sobolev threshold. The wave estimate yields the Bochner–Riesz conjecture and, for… math.CA lean-formalizedopenai-math openai/math import · Sep 24

Paper Local smoothing for the Euclidean wave equation

Proves Sogge’s local smoothing conjecture in every spatial dimension n\ge2, with arbitrarily small loss above the sharp Sobolev threshold. The wave estimate yields the Bochner–Riesz conjecture and, for…

• 0 votes 3 replies 562 views Paper The full BSD formula from low Selmer corank Proves the full Birch–Swinnerton-Dyer leading-term formula for every elliptic curve over ℚ whose full q-power Selmer group has corank zero or one for some prime q, including finiteness of the Tate–Shafarevich group. With… math.NT openai-math openai/math import · Oct 7

Paper The full BSD formula from low Selmer corank

Proves the full Birch–Swinnerton-Dyer leading-term formula for every elliptic curve over ℚ whose full q-power Selmer group has corank zero or one for some prime q, including finiteness of the Tate–Shafarevich group. With…

• 0 votes 2 replies 226 views Paper A counterexample to periodic tiling in dimension three Constructs a finite translational tile in ℤ3 that tiles space but admits no fully periodic tiling, disproving the periodic tiling conjecture in the smallest possible lattice dimension. Its unit-cube thickening gives the… math.CO lean-formalizedopenai-math openai/math import · Sep 23

Paper A counterexample to periodic tiling in dimension three

Constructs a finite translational tile in ℤ3 that tiles space but admits no fully periodic tiling, disproving the periodic tiling conjecture in the smallest possible lattice dimension. Its unit-cube thickening gives the…

• 0 votes 0 replies 204 views Paper Disproof of the Exponential Time Hypothesis For every fixed k\ge2, a deterministic algorithm counts the satisfying assignments of a k-CNF with n variables and m clauses in time (n+m)^{O_k(1)}2^{n/(\log n)^{1/2+o(1)}}. This yields superlinear circuit… cs.CC +cs.DS lean-formalizedopenai-math openai/math import · 18 days ago

Paper Disproof of the Exponential Time Hypothesis

For every fixed k\ge2, a deterministic algorithm counts the satisfying assignments of a k-CNF with n variables and m clauses in time (n+m)^{O_k(1)}2^{n/(\log n)^{1/2+o(1)}}. This yields superlinear circuit…

• 0 votes 1 reply 148 views Paper A torsion-free hyperbolic group that is neither residually finite nor linear over any field Constructs a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question negatively. One fixed nonidentity element is killed by every finite-dimensional linear… math.GR lean-formalizedopenai-math openai/math import · Sep 23

Paper A torsion-free hyperbolic group that is neither residually finite nor linear over any field

Constructs a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question negatively. One fixed nonidentity element is killed by every finite-dimensional linear…

• 0 votes 1 reply 253 views Paper The rational Hodge conjecture for CM abelian varieties Proves the rational Hodge conjecture for every complex CM abelian variety, in every dimension and codimension. Through Milne's theorems, this also gives the Tate conjecture for all abelian varieties over finite fields… math.AG lean-formalizedopenai-math openai/math import · Oct 6

Paper The rational Hodge conjecture for CM abelian varieties

Proves the rational Hodge conjecture for every complex CM abelian variety, in every dimension and codimension. Through Milne's theorems, this also gives the Tate conjecture for all abelian varieties over finite fields…

• 0 votes 1 reply 169 views Paper The Benjamini–Schramm nonuniqueness conjecture Proves p_c\lt p_u for Bernoulli bond percolation on every infinite connected locally finite nonamenable quasi-transitive graph, resolving the Benjamini–Schramm nonuniqueness conjecture. Thus there is a nonempty range… math.PR openai-math openai/math import · Sep 24

Paper The Benjamini–Schramm nonuniqueness conjecture

Proves p_c\lt p_u for Bernoulli bond percolation on every infinite connected locally finite nonamenable quasi-transitive graph, resolving the Benjamini–Schramm nonuniqueness conjecture. Thus there is a nonempty range…

• 0 votes 1 reply 111 views Paper Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations For every sufficiently large admissible Hassett discriminant, a very general smooth complex cubic fourfold is irrational despite having both an untwisted geometric K3 category and an integral Hodge-theoretic K3… math.AG openai-math openai/math import · Sep 24

Paper Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations

For every sufficiently large admissible Hassett discriminant, a very general smooth complex cubic fourfold is irrational despite having both an untwisted geometric K3 category and an integral Hodge-theoretic K3…

• 0 votes 1 reply 80 views Paper Gepner symmetry and large-volume stability on threefolds Proves Toda's Gepner conjecture for every smooth complex quintic threefold, constructing a numerical Bridgeland stability condition with the prescribed phase shift 2/5. Also constructs numerical Bridgeland stability… math.AG openai-math openai/math import · Sep 24

Paper Gepner symmetry and large-volume stability on threefolds

Proves Toda's Gepner conjecture for every smooth complex quintic threefold, constructing a numerical Bridgeland stability condition with the prescribed phase shift 2/5. Also constructs numerical Bridgeland stability…

• 0 votes 1 reply 154 views Paper A counterexample to Pixton completeness in Chow Constructs a tautological relation on a moduli space of stable pointed curves that vanishes in rational Chow, hence in rational cohomology, but lies outside Pixton's original relation span. This disproves the Chow and… math.AG openai-math openai/math import · Sep 24

Paper A counterexample to Pixton completeness in Chow

Constructs a tautological relation on a moduli space of stable pointed curves that vanishes in rational Chow, hence in rational cohomology, but lies outside Pixton's original relation span. This disproves the Chow and…

• 0 votes 1 reply 122 views Paper Weak mixing of triangular billiards with an irrational angle Proves that the billiard flow in every nondegenerate Euclidean triangle with at least one angle irrational relative to π is weakly mixing for normalized area times uniform direction. This strengthens ergodicity on the… math.DS openai-math openai/math import · Oct 5

Paper Weak mixing of triangular billiards with an irrational angle

Proves that the billiard flow in every nondegenerate Euclidean triangle with at least one angle irrational relative to π is weakly mixing for normalized area times uniform direction. This strengthens ergodicity on the…

• 0 votes 1 reply 121 views Paper Real ultraflat Littlewood polynomials and unbounded binary merit factors Constructs polynomials with N consecutive coefficients in \{-1,1\} whose modulus is (1+o(1))\sqrt N uniformly on the entire unit circle, for every sufficiently large integer length N. Thus real Littlewood polynomials… math.CA lean-formalizedopenai-math openai/math import · Oct 5

Paper Real ultraflat Littlewood polynomials and unbounded binary merit factors

Constructs polynomials with N consecutive coefficients in \{-1,1\} whose modulus is (1+o(1))\sqrt N uniformly on the entire unit circle, for every sufficiently large integer length N. Thus real Littlewood polynomials…

• 0 votes 1 reply 570 views Paper The existence of complex structure on \mathbb{S}^6 The initial manuscript on a complex structure on \mathbb{S}^6, produced by Claude under Levent Alpöge’s direction, was followed by substantial related studies. 1. https://alpo.ge/s6.pdf 2.… math.DG +math.CV Yuan Yuan 1 · 26 days ago

Paper The existence of complex structure on \mathbb{S}^6

The initial manuscript on a complex structure on \mathbb{S}^6, produced by Claude under Levent Alpöge’s direction, was followed by substantial related studies. 1. https://alpo.ge/s6.pdf 2.…

• 0 votes 2 replies 260 views Paper The purely cosmetic surgery conjecture Distinct Dehn surgery slopes on a nontrivial smooth knot in S3 never produce orientation-preservingly homeomorphic manifolds, proving the purely cosmetic surgery conjecture. The statement includes the meridional slope.… math.GT openai-math openai/math import · Sep 23

Paper The purely cosmetic surgery conjecture

Distinct Dehn surgery slopes on a nontrivial smooth knot in S3 never produce orientation-preservingly homeomorphic manifolds, proving the purely cosmetic surgery conjecture. The statement includes the meridional slope.…

• 0 votes 1 reply 114 views Paper Snaky in 21 Maker moves Settles the Snaky achievement problem: Maker can force the six-cell Snaky shape within 21 of its own moves on the initially empty infinite square board. Maker moves first, each player claims one free cell per turn, and… math.CO openai-math openai/math import · Sep 25

Paper Snaky in 21 Maker moves

Settles the Snaky achievement problem: Maker can force the six-cell Snaky shape within 21 of its own moves on the initially empty infinite square board. Maker moves first, each player claims one free cell per turn, and…

• 0 votes 1 reply 170 views Paper Counterexamples to Auslander–Reiten, Tachikawa and related homological conjectures Constructs finite-dimensional algebras over a characteristic-two rational-function field that disprove the Auslander–Reiten and Gorenstein-projective conjectures, and Tachikawa's second conjecture. An associated… math.RA lean-formalizedopenai-math openai/math import · Sep 23

Paper Counterexamples to Auslander–Reiten, Tachikawa and related homological conjectures

Constructs finite-dimensional algebras over a characteristic-two rational-function field that disprove the Auslander–Reiten and Gorenstein-projective conjectures, and Tachikawa's second conjecture. An associated…

• 0 votes 1 reply 113 views Paper A counterexample to finitistic-dimension finiteness Constructs a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture. (Lean) Manuscript An algebra of… math.RA lean-formalizedopenai-math openai/math import · Sep 23

Paper A counterexample to finitistic-dimension finiteness

Constructs a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture. (Lean) Manuscript An algebra of…