All OpenAI manuscripts
ManuscriptChoose a manuscript 001-01 · Milne's rationality conjecture for abelian varieties 002-01 · Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank 002-02 · The Selmer converse for elliptic curves at every prime 002-03 · The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one 003-01 · The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane Re s > 7/8 003-02 · The Quasi-Riemann Hypothesis (alternate 11/12 proof) 003-03 · Uniform exclusion of Landau–Siegel zeros 004-01 · Hilbert’s tenth problem over the rational numbers 004-02 · A pointwise 2-converse for elliptic curves with rational two-torsion 005-01 · Catalan's constant is irrational 006-01 · Goldfeld's analytic density conjecture and the 2-converse for elliptic curves 006-02 · The mean analytic rank of quadratic twists of elliptic curves 007-01 · Ordinary two-point correlations of multiplicative functions 008-01 · The Deligne-Drinfeld conjecture 009-01 · Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory 009-02 · Reconstruction from Milnor K-theory modulo the characteristic 009-03 · The Bogomolov-Pop reconstruction theorem 010-01 · Unrestricted pro-modularity at the prime two 010-02 · The Dimension of the Two-Adic Hecke Algebra at Odd Level 010-03 · Fontaine–Mazur modularity at the prime 2 011-01 · Weighted dilation graphs, smooth shifted primes and totient fibers 011-02 · The Poisson-Dirichlet law for prime predecessors 011-03 · Prime Predecessors with an Even Number of Prime Factors 012-01 · The joint Dickman law for consecutive integers 013-01 · The additive indecomposability of the primes 014-01 · Global Arthur Enhancements of Cuspidal Excursion Parameters 014-02 · Rationality of the Canonical Unramified Arthur Filtration 014-03 · Ramanujan-Arthur Decompositions of Cuspidal Functions at Full Finite Level 014-04 · Temperedness at ramified places for globally generic exceptional groups 014-05 · The Restricted Geometric Langlands Equivalence in Positive Characteristic 014-06 · Constructible tame Hecke eigensheaves in positive characteristic 014-07 · Tame Hecke Eigensheaves with Several Marked Points 014-08 · Frobenius Structures on Tame Hecke Eigensheaves 015-01 · Equidistribution of Prime-Degree Torus Packets with Arbitrary Local Type 015-02 · Equidistribution of primitive quartic torus packets for arbitrary orders 015-03 · Equidistribution of Primitive Sextic Torus Packets 016-01 · The abelian Zilber–Pink conjecture 016-02 · The E×CM component of Zilber–Pink for curves in A2 016-03 · Quaternionic division points on curves in the Siegel threefold 016-04 · Elliptic squares and Zilber–Pink for curves in A2 017-01 · The irrationality exponent of pi is 2 018-01 · The Margulis–Platonov conjecture over global function fields 018-02 · The Margulis–Platonov conjecture over number fields 019-01 · Étale covers with a prescribed exterior sheet 019-02 · The p-adic section conjecture 020-01 · Squarefree values of quartics and power-free values of polynomials 021-01 · A quadratic bound for Jacobsthal's function 022-01 · The Weak Inhomogeneous Duffin–Schaeffer Conjecture 023-01 · An unconditional first moment for cubic Gauss sums 024-01 · An asymptotic formula for the number of totients 025-01 · Short Egyptian fractions 026-01 · Positive lower density of large prime gaps 027-01 · Integral points on character varieties of curves 028-01 · Bounded-Step Walks on Gaussian Primes 029-01 · Primitive roots for every admissible integer base 029-02 · Simultaneous primitive roots: a conditional lower bound for prime bases 030-01 · Modularity of elliptic curves over imaginary quadratic fields 031-01 · Open Homomorphisms of Global Solvably Closed Galois Groups 032-01 · The rational Hodge conjecture for CM abelian varieties 032-02 · Algebraic Kuga–Satake correspondences and Hodge conjectures on a K3 quadratic locus 032-03 · Weil classes and Hodge classes on abelian powers 032-04 · Abelian covers, Gale correspondences, and the Hodge conjecture for powers 032-05 · A Conditional Reduction for Algebraic Kuga–Satake Correspondences 033-01 · Orbifold and logarithmic Iitaka subadditivity 033-02 · Logarithmic Kodaira dimension and whole-fiber variation 033-03 · The reverse logarithmic Kodaira inequality and additivity 033-04 · Projective Hodge lines and ordinary Iitaka subadditivity 033-05 · B-semiampleness for compact log-smooth Kähler fibrations 034-01 · Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity 034-02 · Uniform indices for semi-log-canonical log Calabi–Yau pairs 034-03 · Conditional good minimal models for compact Kähler fourfolds 034-04 · Log abundance in characteristic zero 034-05 · Minimal metrics and interior injectivity for nef adjoints 034-06 · Fourfold nonvanishing by minimal metrics and moving jets 034-07 · Lifting sections from the reduced support of an adjoint 034-08 · Schnell fiber spaces and good canonical models 034-09 · Uniform log Iitaka fibrations and bounded moduli denominators 034-10 · Uniform Pluricanonical Iitaka Fibrations 034-11 · Relative denominators and effective systems for log Calabi-Yau fibrations 034-12 · Arithmetic Stein-degree bounds for log Calabi–Yau pairs 034-13 · Uniform effective log Iitaka fibrations for fourfolds 034-14 · Abundance after nonvanishing for compact Kähler fourfolds 035-01 · Log abundance in numerical dimension one for threefolds in positive characteristic 035-02 · Abundance in numerical dimension one for terminal threefolds in positive characteristic 036-01 · Numerical semiampleness of nef adjoint classes on compact Kähler manifolds 036-02 · Numerical Semiampleness of Nef Adjoint Divisors 036-03 · Minimal models and Mori fibre spaces for generalized log canonical Q-pairs 036-04 · Minimal models in numerical dimension one 037-01 · The ordinary-double-point gap in every dimension 037-02 · The normalized-volume gap in dimension four 038-01 · Fujita's freeness conjecture 039-01 · Nagata's conjecture for plane curves 039-02 · Maximal Seshadri constants on arbitrary polarized surfaces 039-03 · Maximal Multipoint Seshadri Constants in Higher Dimensions 039-04 · Maximal multipoint Seshadri constants in positive characteristic 040-01 · Bloch’s conjecture for surfaces with p_g=0 041-01 · Projective-space bases of Lagrangian fibrations 041-02 · The strong hyperkähler SYZ conjecture 042-01 · Every complex K3 surface is Oka 043-01 · P=W in composite rank for fixed determinant 044-01 · The equivariant cohomological Hikita conjecture for arbitrary quivers 046-01 · A projective fourfold with large fundamental group and non-Stein universal cover 046-02 · A surface counterexample to Shafarevich holomorphic convexity 047-01 · An explicit failure of complex affine-space cancellation 048-01 · A singular normal affine surface with free tangent sheaf 049-01 · A stable coordinate that is not a coordinate in four variables 049-02 · An explicit noncoordinate polynomial with affine three-space zero fibre 050-01 · Ample rank-two bundles on the quadric surface without Griffiths-positive metrics 051-01 · Canonical ampleness of compact hyperbolic Kähler manifolds 052-01 · Universal-cover splitting for compact Kähler manifolds 052-02 · Integrability of split tangent bundles on rationally connected manifolds 053-01 · A high-arity counterexample to Pixton completeness in Chow 054-01 · Irrational cubic fourfolds with geometric K3 categories 055-01 · A Gepner stability condition on every smooth quintic threefold 055-02 · Prescribed large-volume charges on threefolds with trivial canonical bundle 056-01 · Termination of generalized log canonical flips on compact Kähler fourfolds 056-02 · Termination of generalized-canonical flips on compact Kähler fourfolds 056-03 · Termination for projective log canonical fourfolds with rational boundary 056-04 · Finite ordinary minimal model programs on compact Kähler fourfolds 056-05 · Finite ordinary minimal model programs on compact Kähler fourfolds 057-01 · The abelianity conjecture for special compact Kähler manifolds 057-02 · Two-step monodromy of special quasi-projective varieties 057-03 · A conditional abelianity theorem for special fourfold pairs with a half-weight divisor 058-01 · Semialgebraic universal covers of normal projective varieties 058-02 · Symmetry of semialgebraic bounded domains with compact quotient 059-01 · Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three 059-02 · Ambiently homeomorphic isolated hypersurface germs in ℂ⁴ with multiplicities four and five 060-01 · Global Spherical Shells on Minimal Surfaces of Class VII 062-01 · Contact Fano manifolds and the LeBrun–Salamon conjecture 063-01 · The generalized Mukai conjecture 064-01 · Topological triviality of mu-constant families of surface singularities 065-01 · Virasoro Constraints under Projectivization 065-02 · Virasoro Constraints for Projective Complete Intersections 066-01 · Bounded klt complements for Fano contractions 066-02 · Uniform Cartier sections for Fano type contractions 067-01 · The Campana–Peternell conjecture in dimension six 068-01 · Anticanonical nonvanishing from smooth semipositivity 068-02 · Invariant anticanonical indices and conversion of twisted differentials 068-03 · Bounded anticanonical metrics on klt pairs and torus quotients 068-04 · Cohomological transfer and equivariant anticanonical sections 068-05 · Metric descent and rank-preserving contractions 068-06 · Integrable metrics and effectivity with controlled boundary 068-07 · Exact orders and invariant anticanonical linear systems 069-01 · Global quantum geometric Langlands at irrational level 071-01 · Removable Boundaries and Rigidity of Circle Domains 071-02 · Koebe's Circle-Domain Conjecture 072-01 · Brennan's conjecture and sharp inverse-square integral means 072-02 · A strict inverse-first-power bound for univalent functions 073-01 · The Falconer distance conjecture in all dimensions 074-01 · The Kakeya maximal conjecture in three dimensions 074-02 · Every four-dimensional Kakeya set has full Hausdorff dimension 075-01 · Almost-everywhere Fourier convergence in L log L 076-01 · Ultraflat real Littlewood polynomials 076-02 · Nearly minimal maxima and positive minima of Littlewood polynomials 076-03 · Asymptotically minimal maxima of real Littlewood polynomials 077-01 · Elliptic capacity propagation and Fourier restriction to the sphere 077-02 · Diagonal Fourier extension for positively curved surfaces in three dimensions 078-01 · Bochner–Riesz multipliers in three dimensions 079-01 · Critical local smoothing for the three-dimensional wave equation 080-01 · Endpoint convergence for the planar Schrodinger equation 080-02 · Endpoint pointwise convergence for the Schrodinger equation in higher dimensions 081-01 · Riesz transforms and uniform rectifiability in higher codimension 082-01 · Annular variation of the triangular Hilbert transform at the symmetric point 082-02 · An L³ bound for the dyadic triangular Hilbert form 082-03 · The maximal triangular Hilbert transform at the symmetric point 083-01 · A uniform Hilbert transform estimate for Lipschitz directions 084-01 · The geometric case of the Erdős similarity conjecture 084-02 · The dyadic case of the Erdős similarity conjecture 085-01 · An Endpoint Gradient Bound for the Centered Disk Maximal Operator 086-01 · An L^3 bound for the trilinear Hilbert transform 087-01 · The symmetric Mahler conjecture and its equality cases 087-02 · The Mahler Conjecture for General Convex Bodies 087-03 · Symplectic Balls in Symmetric Polar Products 088-01 · Petty’s projection-volume conjecture in dimensions at least four 088-02 · A product counterexample to the simplex maximum for projection-body volume 089-01 · Planar Graph Metrics Embed into L1 with Constant Distortion 089-02 · L1 Embeddings of Graphs of Bounded Treewidth 090-01 · An atomic certificate for triangular-lattice universal optimality 090-02 · Universal optimality of the triangular lattice 090-03 · A sharp Fourier certificate for planar circle packing 090-04 · Triangular minimality for planar Coulomb renormalized energy 091-01 · The logarithmic Brunn–Minkowski conjecture 092-01 · A single-lattice covering bound of order n log n 092-02 · Translative covering densities of order n log n 093-01 · A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures 094-01 · Subpolynomial dimension reduction in Lp 095-01 · Hyperbolicity Cones Without Semidefinite Lifts 095-02 · A nonspectrahedral hyperbolicity cone 095-03 · An Exact Semidefinite Lift of a Nonspectrahedral Hyperbolicity Cone 096-01 · The Gaussian propeller bound in every dimension 097-01 · The Euclidean Steinitz–Bergström theorem 098-01 · A doubling Hilbert subset with no finite-dimensional bi-Lipschitz embedding 099-01 · Edit Distance in l1: Matching Bounds up to Constants in the Exponent 099-02 · Finite-Circle Obstructions, Binary Codes, and Histogram Embeddings for Edit Distance 099-03 · Tree Constructions for the l1 Distortion of Binary Edit Distance 100-01 · Finite angular cylinder covers below the half-area bound 100-02 · Finite cylinder approximation of ruled sets 100-03 · Slope-field perturbations of the two-cylinder covering 100-04 · Finite triangular approximation of radial sweeps 101-01 · A sharp entropy bound and the simplex inequality for isotropic constants 102-01 · The Unique Games Theorem 102-02 · A Direct Proof of Optimal Max-Cut Hardness 102-03 · The Factor-Two Hardness Threshold for Vertex Cover 102-04 · Constant-factor hardness of Min-UnCut 102-05 · Constant-factor hardness of directed feedback vertex set 103-01 · Exact derandomization of logarithmic space: L = RL = BPL 104-01 · Turn-Based Stochastic Mean-Payoff Games in Deterministic Quasipolynomial Time 104-02 · Mean-payoff parity games in quasipolynomial time 104-03 · Deterministic quasipolynomial-time mean-payoff games 104-04 · Randomized quasipolynomial-time mean-payoff games 105-01 · Perfect completeness for 2-to-1 games 106-01 · Hardness of finding large independent sets in three-colorable graphs 107-01 · An Upper Bound of 9/4 for the Matrix Multiplication Exponent 107-02 · Complex Matrix Multiplication Below 2.258 and Rectangular Bounds 107-03 · Staggered extraction for exact matrix multiplication over every field 108-01 · A cubic lower bound for border determinantal complexity of the permanent 109-01 · Integer multiplication below n log n 110-01 · Squared-logarithmic randomized k-server on arbitrary metrics 110-02 · Uniform computation of the squared-logarithmic k-server bound 111-01 · One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary 112-01 · Beyond the Square-Root Exponent for Depth-Three Boolean Circuits 113-01 · A Fully Polynomial Randomized Approximation Scheme for Perfect Matchings in General Graphs 113-02 · Entropy and Face Dimension of the Perfect-Matching Polytope 114-01 · An FPRAS for Common Integer Polymatroid Bases with Binary Capacities 114-02 · Approximate counting of common bases of two matroids 115-01 · Exact Uniform Sampling of Contingency Tables with Arbitrary Margins 115-02 · An FPRAS for Cell-Bounded Contingency Tables 116-01 · Uniform Matrix Hitting Points in Every Positive Characteristic 116-02 · One Rational Matrix Hitting Point for Noncommutative Formulas 116-03 · Polynomial Hitting Lists for Noncommutative Rational Formulas 117-01 · Constant-factor hardness of uniform sparsest cut 117-02 · Near-square-root logarithmic integrality gaps for uniform sparsest cut 118-01 · Additive hardness and unbounded configuration gaps in bin packing 119-01 · Sharp binary-information contraction on the discrete cube 119-02 · Hellinger contraction with arbitrary Boolean output bias 120-01 · Almost-Linear-Time Maximum-Cardinality Matching in General Graphs 121-01 · An Almost-Linear Approximation Scheme for Edit Distance 122-01 · Uniform quasipolynomial-time trace reconstruction 122-02 · A latest-anchor induction with spectrally compact masks for worst-case trace reconstruction 122-03 · Quantitative lower bounds for trace reconstruction 124-01 · A Polynomial-Time Algorithm for Three-Machine Unit-Job Scheduling 125-01 · Single-exponential recovery and bounded-price strictness for metric k-median 125-02 · The approximation threshold for metric k-median 126-01 · Exponential PSD rank of positively shifted matching matrices 127-01 · Average sensitivity of polynomial threshold functions 128-01 · A Polynomial-Time 2-Approximation for Shortest Common Superstring 129-01 · An exponential state lower bound for two-way nondeterministic complementation 129-02 · An exponential two-way deterministic state lower bound for one-way liveness 130-01 · An explicit power saving for the exact discrete Fourier transform 130-02 · Finite tensor savings and exact Fourier circuits 131-01 · Polynomial mixing of the switch chain for every graphical degree sequence 132-01 · A superquadratic separation between sensitivity and block sensitivity 133-01 · Parity lifts and bounded-treewidth witnesses for Weisfeiler–Leman equivalence 133-02 · The complexity of identifying a graph by Weisfeiler–Leman refinement 133-03 · Unconditional time lower bounds for Weisfeiler–Leman equivalence 133-04 · Variable-dimension Weisfeiler–Leman equivalence on general and subcubic graphs 134-01 · Finite Monoid Computations and a Uniform Generalized Star-Height Bound 134-02 · Generalized Star Height at Most Four 134-03 · Generalized Star Height at Most Three 135-01 · Homogeneous depth-five lower bounds for iterated matrix multiplication 136-01 · The PCP-for-PPAD conjecture: a quasilinear reduction 137-01 · Simulating One-Tape Time in Two-Fifths-Power Space 138-01 · Subset Sum in Time O(2^{0.49n}) 138-02 · A Low-Space Algorithm for Worst-Case Subset Sum 139-01 · Subpolynomial query complexity for well-conditioned log-concave sampling 140-01 · Memory and precision in noiseless Gaussian regression 140-02 · Posterior replicas and conditional information in Gaussian regression 140-03 · Localization costs and information growth for exact Gaussian observations 140-04 · Projection moments, positive cap domination, and Riesz estimates on the sphere 140-05 · Replacing Gaussian observations in memory-constrained inference 140-06 · Subsphere methods for memory-sample lower bounds in noiseless Gaussian regression 141-01 · Existential–universal real sentences in the counting hierarchy 142-01 · Deterministic Polynomial Factorization over Prime Fields 143-01 · Uniform bounds for planar polynomial limit cycles 143-02 · Two limit cycles for quintic Liénard systems 144-01 · A smooth three-torus diffeomorphism with simple Lebesgue spectrum 145-01 · Rokhlin's multiple-mixing problem for one transformation 146-01 · Positive Metric Entropy for the Standard Map at Large Parameters 147-01 · Continuous Phase Foliations Create Analytic Caustic Collars 147-02 · Rigidity of Smooth Billiards with a Continuous Caustic Collar 148-01 · The entropy-rate dimension formula for self-similar measures on the line 149-01 · Uniform Permanence in Weakly Reversible Mass-Action Systems 149-02 · Boundedness and persistence of weakly reversible mass-action systems 150-01 · Weak mixing of triangular billiards with an irrational angle 150-02 · Ergodicity of triangular billiards with an irrational angle 151-01 · A C^1 Counterexample to the Entropy Conjecture 152-01 · A zero-entropy system without a smooth positive-volume model 153-01 · Arithmetic classification and non-Pisot singularity for Bernoulli convolutions 154-01 · Pointwise Multiple Ergodic Averages for Mixing Transformations 154-02 · Pointwise convergence of fourfold ergodic averages for mixing transformations 154-03 · Triple ergodic averages with distinct integer slopes 154-04 · Pointwise convergence of triple ergodic averages for mixing transformations 155-01 · A translational tile with no fully periodic tiling in dimension three 156-01 · A nine-dimensional counterexample to Borsuk's covering assertion 157-01 · A counterexample to Hadwiger's conjecture 157-02 · A counterexample to the Colin de Verdière chromatic conjecture 157-03 · A linear list-coloring bound in terms of the Hadwiger number 158-01 · The Euclidean plane is not five-colorable 159-01 · Quasipolynomial Bounds for Arithmetic Progressions 160-01 · Quantitative Superexponential Bounds for van der Waerden Numbers 161-01 · A counterexample to Sidorenko's conjecture 162-01 · Balanced counterexamples to Ryser's conjecture at prime orders 162-02 · A counterexample to Ryser's covering conjecture 164-01 · Monochromatic finite sums and products in the positive integers 165-01 · The crossing number of complete graphs 165-02 · The crossing number of complete bipartite graphs 166-01 · The higher-dimensional Erdős distinct-distances conjecture 167-01 · The weak pinned planar distance theorem 167-02 · A power saving for planar unit distances 168-01 · Combinatorial invariance of Kazhdan–Lusztig polynomials 169-01 · Elementary positivity of chromatic quasisymmetric functions 170-01 · The sharp logarithmic exponent of r(5,t) 170-02 · Sharp logarithmic exponents for fixed off-diagonal Ramsey numbers 171-01 · The hypercube Ramsey number has linear order 172-01 · A classification of finite Euclidean Ramsey configurations 173-01 · A proof of Seymour’s second-neighborhood conjecture 174-01 · The strong thin tree conjecture 174-02 · A polynomial-time construction of strong thin trees 175-01 · Graph Decompositions at the Integral Expectation Threshold 175-02 · Integral and fractional expectation thresholds are equivalent 175-03 · Talagrand’s discrete-convexity conjecture 176-01 · The second Kahn–Kalai conjecture 177-01 · Bounded-degree coboundary expanders in every dimension 178-01 · Deterministic nonbipartite Ramanujan graphs in every fixed degree 179-01 · The circulant Hadamard conjecture 180-01 · Paired states and Hamiltonian cycles in cubic bipartite planar graphs 181-01 · A linear cycle-and-edge decomposition of every graph 182-01 · A power saving for intersective polynomial differences with an exponent depending only on the degree 182-02 · A Power Saving for Polynomial Differences at Prime Arguments 182-03 · A power saving for square-difference-free sets 183-01 · A power saving for planar halving lines 184-01 · Correspondence coloring graphs with a forbidden clique 184-02 · A logarithmic independence bound for clique-free graphs 185-01 · A Counterexample to the Infinite Matroid Packing/Covering Conjecture 186-01 · A uniform influence bound for hypergraph properties 186-02 · A Sharp Threshold Bound for Monotone Graph Properties 187-01 · Snaky in 21 Maker moves 188-01 · The sharp terminal leave in random triangle removal 189-01 · Cycle--clique Ramsey numbers 190-01 · Polynomial removal fails for ordered binary matrices 191-01 · A power improvement in the Heilbronn triangle lower bound 192-01 · Unbounded Violations of the Square-Root Degree Bound 193-01 · Positivity of Serre's Intersection Multiplicity 194-01 · Lech's multiplicity conjecture 195-01 · A Complete Local Domain without a Small Cohen–Macaulay Module 196-01 · A Torsion-Free Group Algebra with Zero Divisors 197-01 · A Torsion-Free Group Algebra That Is Not Directly Finite 197-02 · A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Characteristic Two 197-03 · A Counterexample to the Group-Ring Determinant Conjecture 197-04 · A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Odd Characteristic 198-01 · An algebra of infinite little finitistic dimension 199-01 · An explicit counterexample to the Auslander-Reiten conjecture 199-02 · A counterexample to Tachikawa's second conjecture 200-01 · The Artinian Lex-Plus-Powers Betti Theorem 200-02 · Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture 201-01 · A Counterexample to Kurosh’s Division-Ring Problem 202-01 · The Blockwise Alperin Weight Conjecture 203-01 · Donovan's Conjecture over Algebraically Closed Fields 203-02 · Integral Donovan Finiteness over Witt Vectors 204-01 · Tensor saturation for even spin groups 205-01 · Universal Tensor Squares for Symmetric Groups 205-02 · A Cyclic Polytabloid Proof of Saxl's Conjecture 206-01 · Finite congruence lattices: characterization and undecidability 206-02 · A negative solution to the finite lattice representation problem 207-01 · The ℓ¹-Bass Conjecture for Discrete Groups 207-02 · The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture 208-01 · Fiber functors for finite symmetric tensor categories in positive characteristic 209-01 · An integral counterexample to Gersten's conjecture 209-02 · An integral degree-three Gersten counterexample 210-01 · Foulkes' conjecture for the sixth symmetric power 210-02 · Quadratic stabilization of the canonical Foulkes--Howe map 211-01 · Random Walks on Critical FK–Ising Maps and Liouville Brownian Motion 211-02 · Spectral convergence for critical FK–Ising planar maps 211-03 · A Linear Clock for Random Walk on Tree-Weighted Planar Maps 211-04 · Canonical conformal limits of subcritical FK planar maps 211-05 · The critical Liouville quantum sphere and geometric limits of FK maps at q=4 211-06 · Metric-measure limits of subcritical FK and spanning-tree planar maps 211-07 · Brownian continuum random tree limits of finite Fortuin–Kasteleyn maps above four 212-01 · No bigeodesics in planar first-passage percolation 212-02 · Strict convexity and differentiability of the planar exponential first-passage limit shape 213-01 · Critical bond and site percolation on the cubic lattice 213-02 · No percolation at criticality on quasi-transitive graphs 214-01 · Nonuniqueness of percolation on nonamenable quasi-transitive graphs 215-01 · The canonical massive continuum limit of the two-dimensional O(3) model 215-02 · An Isolated Particle Pole for the Two-Dimensional O(3) Spin Field 215-03 · Exact mass asymptotics for the two-dimensional O(4) lattice model 215-04 · Sharp mass bounds for the two-dimensional O(4) model 215-05 · Exponential decay in two-dimensional classical O(n) models 216-01 · The critical logarithmic correction for the planar XY model 216-02 · Critical Center Magnetization in the Planar XY Model 216-03 · The Critical Spin Field of the Planar XY Model 216-04 · Essential Singularity of the Correlation Length in the Planar XY Model 216-05 · The critical correlation exponent of the planar XY model 216-06 · BKT universality for height and planar spin fields 217-01 · The low-temperature Sherrington–Kirkpatrick free-energy limiting law 217-02 · The low-temperature Sherrington–Kirkpatrick fluctuation scale 218-01 · Quenched SLE₃ limits for general weak random-bond Ising models 218-02 · Quenched SLE₃ Universality for the Weak Random-Bond Ising Model 218-03 · Logarithmic Relative Fluctuations in the Weakly Disordered Planar Ising Model 218-04 · Conformal universality of bulk Ising correlations under weak interactions 218-05 · SLE3 universality for weak finite-range Ising interactions 218-06 · Buffered comparison and stopping-band resolution in critical Ising 219-01 · Fixed-energy universality for weak Anderson disorder on random regular graphs 219-02 · GOE bulk universality for fixed-degree random regular graphs 220-01 · A directional zero–one law for finite-range-dependent random environments 220-02 · A directional zero–one law under strict ellipticity 220-03 · Directional transience implies ballisticity 221-01 · The Mézard–Parisi formula for diluted spin glasses 222-01 · The free energy of the Ising random perceptron 222-02 · Microscopic jamming in the negative spherical perceptron 222-03 · The spherical perceptron with bi-orthogonally invariant disorder 222-04 · The free energy of the spherical random perceptron 223-01 · Square-lattice FK interfaces and nested loops for 1 <= q < 4 223-02 · Self-dual random-cluster interfaces below one 223-03 · Quenched SLE Universality for Weakly Disordered FK–Ising Interfaces 223-04 · Thermal FK–Ising interfaces and massive SLE 223-05 · Natural Occupation Measures for Critical Square-Lattice FK Interfaces 223-06 · Conformal Limits of Critical Square-Lattice Random-Cluster Interfaces 224-01 · From critical crossings to quenched near-critical universality in Voronoi percolation 224-02 · A Pivotal Amplitude for Voronoi Percolation from Cardy's Formula 224-03 · Cardy’s formula for critical Poisson–Voronoi percolation 225-01 · The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2) 226-01 · The curve scaling limit of half-plane double dimers 227-01 · Universality of critical quench autocorrelations in the Sherrington–Kirkpatrick model 227-02 · Functional universality of critical SK autocorrelations 227-03 · A spectral gap throughout the high-temperature Sherrington–Kirkpatrick phase 227-04 · Cutoff throughout the high-temperature Sherrington–Kirkpatrick phase 227-05 · Critical slowing down in the Sherrington–Kirkpatrick model 227-06 · Stretched-exponential barriers for typical SK initial states 227-07 · A typical-start upper bound for low-temperature SK Glauber dynamics 227-08 · Critical mixing in the Sherrington–Kirkpatrick model 228-01 · A continuum temperature singularity for a radial pair potential 228-02 · A radial continuum phase transition with algebraic decay 229-01 · The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model 229-02 · A Capacity Criterion for Four-State Potts Reconstruction on Trees 229-03 · The exact reconstruction threshold for the three-state symmetric channel 230-01 · An exact Hausdorff gauge for SLE 230-02 · An explicit exact Hausdorff gauge for SLE 231-01 · The free uniform spanning forest is a factor of IID 232-01 · Gaussian free-field limits of weighted integer Lipschitz heights 232-02 · The Gaussian free field limit of integer Lipschitz heights with two-arc boundary data 232-03 · Uniform real Lipschitz surfaces on the triangular lattice 233-01 · The joint scaling limit of critical Ashkin-Teller currents 234-01 · All-temperature pressure for orthogonally invariant Ising spin glasses 235-01 · A Limiting Satisfiability Threshold for Every Fixed Clause Size 235-02 · Linear Variance of the Random 3-SAT Hitting Time 235-03 · Variance of the Random k-SAT Hitting Time 235-04 · Computing the Random 3-SAT Threshold 236-01 · The sharp factor-of-IID threshold for the free Ising model on regular trees 237-01 · Radial transfer estimates and polygon length laws for honeycomb walks 237-02 · Critical honeycomb chords with prescribed boundary endpoints 237-03 · Cylinder loop weights and planar nesting 237-04 · Mass and covering exponents for fixed-length honeycomb walks 237-05 · Signed cylinder propagation and marked polygons on the honeycomb lattice 237-06 · Cylinder amplitudes and logarithmic bridge-length windows on the honeycomb lattice 237-07 · Marked polygon correlations and one-arc bounds 237-08 · Disk transfer representations and confined bridge mass 237-09 · Polynomial vacuum representations and bridge mass for honeycomb walks 237-10 · Renewal and changes of law for critical honeycomb walks 237-11 · Critical strip-crossing mass on the honeycomb lattice 237-12 · Uniform marked-polygon estimates and sharp finite bridge moments 237-13 · Cap-selected amplitudes and triangle chords for honeycomb walks 238-01 · Optimal-order mixing of the Thorp shuffle 238-02 · Random coordinate frames and partial permutation laws 238-03 · From partial permutation information to Fourier bounds 238-04 · Conditional information under deterministic coordinate sweeps 238-05 · Conditional permutations in a revealed switching environment 238-06 · Routing densities and representation contraction for Thorp sweeps 238-07 · Row–column symmetry and contraction of coordinate sweeps 238-08 · Random-subspace tests and trace smoothing for coordinate sweeps 238-09 · Compatibility entropy and the spectrum of a Thorp sweep 238-10 · Signed tensor densities and diagram budgets for the Thorp shuffle 238-11 · Conditional coordinate sweeps and analytic transfer 238-12 · A strict four-row permanent inequality and permutation moments 239-01 · The sharp exponential rate of singularity for symmetric Bernoulli matrices 239-02 · The sharp singularity rate for biased symmetric sign matrices 240-01 · A CH obstruction to a prescribed categoricity threshold 240-02 · Eventual categoricity for abstract elementary classes 241-01 · Rigidity of the Turing degrees 242-01 · Single-fold Diophantine representations 243-01 · Choiceless polynomial time with counting does not capture polynomial time 243-02 · Witnessed symmetric choice is strictly stronger than choiceless polynomial time with counting 244-01 · The Partition Principle does not imply Choice 245-01 · Weak and strong normalization in pure type systems 246-01 · A Modulus Proof of Cannon’s Conjecture 247-01 · An infinite finitely presented residually finite 2-group 247-02 · An infinite finitely presented periodic group 248-01 · Thompson's group F is nonamenable 249-01 · A finitely generated counterexample to the Eilenberg–Ganea conjecture 250-01 · Finite algebraic envelopes and the Boone–Higman conjecture 250-02 · Simple F∞ overgroups of groups with decidable word problem 250-03 · A universal group of type F∞ 251-01 · Unitarizability implies amenability for discrete groups 251-02 · Strong Ulam Stability Characterizes Amenability 252-01 · A torsion-free hyperbolic group that is not residually finite 253-01 · An infinite finitely presented simple amenable group 254-01 · Harmonic heights and the Artin K(pi,1) conjecture 254-02 · An Artin group with no geometric CAT(0) action 254-03 · Parabolic intersections in Artin groups 255-01 · Quasi-isometric recognition of virtually polycyclic groups 256-01 · Nonsingular systems of equations over arbitrary groups 256-02 · The Kervaire theorem for groups 257-01 · A hyperbolic group with no geometric CAT(0) action 258-01 · Baumslag-Solitar-free one-relator groups are hyperbolic 258-02 · Virtual compact specialness of hyperbolic one-relator groups 259-01 · A group without fixed price 260-01 · The spacetime Penrose inequality with charge and original-data rigidity 260-02 · A Charged Reduction of the Spacetime Penrose Inequality in Spatial Dimensions at Least Four 260-03 · Spacetime Penrose inequalities: enclosing area, charge, and rigidity 260-04 · The Kerr–Newman Penrose Inequality for Axisymmetric Electrovacuum Exteriors 260-05 · Electromagnetic tails and the Kerr–Newman Penrose inequality 260-06 · The nonmaximal anti-de Sitter Penrose Inequality and original-data rigidity 260-07 · The Penrose inequality for maximal asymptotically hyperbolic initial data 260-08 · A local Penrose inequality for conformal perturbations of Schwarzschild–anti-de Sitter data 260-09 · The spacetime Penrose inequality and enclosing area 260-10 · Conformal flow and the Riemannian Penrose inequality with minimizing frontiers 260-11 · Equality and rigidity in the spacetime Penrose inequality 260-12 · Boundary graph deformations for the spacetime Penrose inequality 260-13 · Area-controlled end replacement and the Bondi Penrose inequality in the CKS class 261-01 · Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three 261-02 · Pure-Point Spectrum for the Two-Dimensional Anderson Model at Every Positive Disorder 262-01 · Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality 262-02 · Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials 262-03 · Sharp one-dimensional Lieb–Thirring constants 263-01 · Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms 263-02 · Generalized ionization energies for full Coulomb atoms 263-03 · Generalized outer-electron radii of neutral Coulomb atoms 264-01 · Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime 264-02 · Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes 264-03 · Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility 265-01 · A two-dimensional area law from a global spectral gap 265-02 · Polynomial PEPS approximation of gapped square-grid ground states 266-01 · The maximum number of mutually unbiased bases in dimension six 266-02 · Exact Fourier certificates for complex Hadamard matrices of order six 267-01 · Bose–Einstein condensation at positive temperature in the dilute hard-sphere gas 267-02 · Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas 267-03 · Quantum Depletion for Fixed Bounded Repulsive Potentials 267-04 · A density-uniform condensate bound for dilute Bose gases 267-05 · Ground-state condensation in the dilute hard-sphere gas 268-01 · The periodic spin-one Haldane gap 268-02 · A boundary-field gap for the spin-one Heisenberg chain 269-01 · Uniform Stability of the Spherical Laughlin Gap 269-02 · A Fock-space inequality and the Laughlin spectral gap 270-01 · The unique threshold bound state of the SU(N) BFSS model 270-02 · Positive eigenvalues of the relative SU(2) BFSS Hamiltonian 271-01 · Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions 271-02 · The first lattice correction to Bloch's law 271-03 · The spherical magnetization law for the three-dimensional quantum Heisenberg ferromagnet 271-04 · Spontaneous magnetization in the quantum Heisenberg ferromagnet 272-01 · Entanglement with zero distillable secret key in local dimension ten 273-01 · The entropy photon-number inequality 274-01 · Product-projection localization and the QAC0 parity lower bound 274-02 · Regular trajectories, pruning and quantum parity 275-01 · Continuum Coulomb hardness with binary nuclear charges 275-02 · QMA-hardness of continuum Coulomb energy with unit nuclear charges 276-01 · Classical capacity and entropy inequalities for generalized amplitude damping 277-01 · Threshold parallel repetition for finite-dimensional entangled games 278-01 · A Coulomb ground-state density without Kohn-Sham ensemble representation 279-01 · Exact quantum factoring over a fixed finite gate set 280-01 · Strongly rational unitary vertex operator algebras and conformal nets 281-01 · QAOA attains the SK ground-state energy in the thermodynamic-first limit 281-02 · Full support of the zero-temperature Sherrington-Kirkpatrick order parameter 282-01 · Scale and conformal symmetry in four-dimensional operational quantum field theory 283-01 · Polynomial-Time Unitary Synthesis from a Boolean Oracle 284-01 · A Nearly Quartic Separation Between Randomized and Quantum Query Complexity 285-01 · A torsion-free counterexample to reduced Baum–Connes injectivity 285-02 · A torsion-free counterexample to the Kadison–Kaplansky projection conjecture 285-03 · An irrational-trace counterexample to reduced Baum–Connes 286-01 · Arithmeticity of twisted finite correspondences for lattices over local fields 286-02 · The arithmetic category and stable recovery of lattice factors 287-01 · An isomorphism of the free group factors 288-01 · Kadison's similarity theorem through uniform derivation estimates 289-01 · Universal strong Kadison–Kastler stability 289-02 · Near Inclusions of von Neumann Algebras Without Small Spatial Embeddings 289-03 · Close Separable C*-Algebras Without Spatial Conjugacy 290-01 · Expected amenable subalgebras preserving core commutants 290-02 · Bounded recovery for modular spectral averages 291-01 · Equivariant Jiang–Su Stability for Amenable Actions in the Unital Stably Finite Case 291-02 · Cuntz comparison and Jiang–Su absorption 291-03 · Nuclear dimension and Jiang–Su stability without elementary subquotients 291-04 · Tracial projection methods and uniform property Gamma 292-01 · An explicit obstruction to nuclear norm-ultrapower embeddings 293-01 · Invariant-projection counterexamples for every irrational rotation 293-02 · Backward intertwiners and a transitive commutant 294-01 · A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness 295-01 · Vanishing of higher bounded Hochschild cohomology 296-01 · Relative generation and the generator problem for finite factors 297-01 · A counterexample to Naimark's problem in ZFC 298-01 · A finite-entropy separation of microstates and nonmicrostates free entropy 299-01 · The Kirchberg–Rørdam character criterion 300-01 · Approximation Paving over Arbitrary Maximal Abelian Subalgebras 300-02 · Quadratic Strong-Operator Paving over Arbitrary Maximal Abelian Subalgebras 301-01 · The trace cone classifies Razak–Jacelon stabilizations 302-01 · Filtered products and boundary-preserving compression in complex cobordism 302-02 · Radius of comparison equals half the mean dimension 303-01 · Weak pure infiniteness and O-infinity absorption 304-01 · The Hilbert–Smith conjecture in every finite dimension 305-01 · A boundary-only obstruction to four-dimensional disk embedding 305-02 · A marked tensor obstruction to four-dimensional disk embedding 305-03 · A PD4 group without an aspherical manifold model 306-01 · Purely cosmetic surgery on knots in the three-sphere 307-01 · Failure of rational injectivity for maximal coarse assembly 307-02 · A counterexample to the coarse Novikov conjecture 308-01 · Finite Smith–Toda Complexes at Varying Primes 308-02 · A finite Smith–Toda complex V(4) at the prime 1009 309-01 · The Kervaire invariant problem at the prime three 310-01 · Rational homology and Quillen's conjecture 311-01 · Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra 312-01 · The Grothendieck homotopy hypothesis via elementary expansions 313-01 · Finite generation for the K(n)-local sphere 314-01 · Cyclic length and chromatic fixed-point loss 315-01 · The Singer conjecture in dimension four 316-01 · The Stable Hurewicz Image of the Sphere at Two 317-01 · Thomason Model Structures in Every Strict Higher Dimension 318-01 · Filtered chromatic splitting at generic primes 318-02 · The height-three chromatic overlap: an explicit filtration and its attachments 318-03 · A rational obstruction to strong chromatic splitting at height three 318-04 · Failure of finite assembly for a chromatic overlap at the prime three 318-05 · Counterexamples to weak chromatic splitting: sphere kernels and descent exponents 319-01 · Counterexamples to the Hahn-Wilson conjecture at height two 320-01 · Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type 321-01 · A Counterexample to Wall's D(2) Problem 322-01 · A positive solution to Tingley’s problem 323-01 · Relative independence of the separable quotient problem 324-01 · Lipschitz Equivalent Separable Banach Spaces Need Not Be Linearly Isomorphic 324-02 · Bi-Lipschitz Absorption of c0 Without a Linear Copy of c0 325-01 · A direct proof of the complete Crouzeix inequality 325-02 · The complete Crouzeix theorem: optimal similarity and a common positive boundary representation 326-01 · The cotype–cotype conjecture under the approximation property 327-01 · Nontrivial Markov Type Forces Superreflexivity 328-01 · Fixed Points of Nonexpansive Maps in Reflexive Banach Spaces 329-01 · Counterexamples to the duality conjecture for metric entropy 330-01 · A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces 331-01 · Asymptotic midpoint uniform convexity and unbounded diamond distortion in a reflexive tree space 331-02 · Midpoint lenses in segment spaces 331-03 · Distortion of countably branching diamonds from midpoint and tree energies 331-04 · Exact asymptotic moduli in a Daugavet subspace of L1 331-05 · Midpoint convexity from bounded tree potentials and path costs 331-06 · Independent products in real L1: asymptotic midpoint convexity without AUC renormings 331-07 · Midpoint convexity from two recursive potentials 332-01 · Metric Markov Cotype Two of ℓ_1 333-01 · Smooth isometric immersions of closed surfaces into Euclidean four-space 334-01 · A Smooth Metric with No Local Isometric Immersion into Three-Space 335-01 · An integral scalar curvature bound for real simplicial volume 335-02 · Positive scalar curvature forces rational inessentiality 336-01 · Spectral scalar curvature and uniform Urysohn width 336-02 · Spectral scalar curvature and Urysohn width in dimension three 336-03 · Positive scalar curvature and uniform codimension-two width 337-01 · Generalized Cartan–Hadamard isoperimetry and Euclidean equality rigidity 337-02 · Sharp integral fillings in CAT(0) spaces 338-01 · Uniformization of complete Kähler manifolds with positive bisectional curvature 339-01 · Entropy equality and local symmetry in negative curvature 340-01 · A counterexample to the nearby Lagrangian conjecture 341-01 · Deforming hypersymplectic four-manifolds to hyperkähler triples 342-01 · Taming implies compatibility on four-manifolds 343-01 · Symplectic Ball Packings in Higher Dimensions 344-01 · The metric Blaschke theorem 345-01 · Infinitely many closed geodesic images on every Riemannian sphere 346-01 · A Codimension-One Bound for the Singular Set of a Stationary Integral Varifold 346-02 · Almost-everywhere regularity of stationary integral varifolds 347-01 · Hamiltonian Fixed Points Below the Stable Morse Number in Dimension Twenty-Two 347-02 · Sharpness of the Cyclic Integral Floer Bound Below the Stable Morse Number 347-03 · Hamiltonian Fixed Points Below the Stable Morse Number 347-04 · A nondegenerate counterexample to the Morse-number Arnold bound 347-05 · Three fixed points on the symplectic quadric threefold 348-01 · Zero-Plane Rigidity for Einstein Four-Manifolds 348-02 · An L² Einstein Gap for Nonnegatively Curved Four-Manifolds 348-03 · Positively curved Einstein four-manifolds 349-01 · The Solomon–Yau least-volume theorem 350-01 · Sharp nodal length on smooth surfaces 350-02 · Smooth counterexamples to Yau's nodal upper bound in dimensions three and four 350-03 · Power-law violations of Yau's nodal upper bound 351-01 · A closed Ricci flow with bounded scalar curvature and finite-time curvature blowup 351-02 · Bounded scalar curvature and smooth extension of four-dimensional Ricci flow 351-03 · Path selection and an elliptic inequality on degenerating Ricci-flat trees 352-01 · A finite-time singularity of Calabi flow on projective space 353-01 · A Smooth Nonquadratic Entire Affine Maximal Graph in Dimension Ten 353-02 · The affine Bernstein theorem in dimensions three through nine 354-01 · The Isoperimetric Conjecture for the Cubic Flat Three-Torus 355-01 · Uniqueness of tangent flows at the first singular time of embedded surface mean-curvature flow 356-01 · Gigli’s distributional curvature characterization of Alexandrov spaces 356-02 · Weak Hessian bounds along every geodesic in RCD spaces 357-01 · Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces 358-01 · A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric 359-01 · A negatively pinched Kähler threefold without bounded holomorphic coordinates 359-02 · One-sided negative sectional curvature and the holomorphic Liouville property 360-01 · Global Support and Convex Injectivity Domains under Weak MTW 360-02 · Uniform Bi-Holder Transport from Weak MTW 361-01 · A counterexample to integer-degree harmonic dimension comparison 361-02 · A Three-Dimensional Counterexample to Integer-Degree Harmonic Dimension Comparison 362-01 · Global classical solutions of the three-dimensional relativistic Vlasov–Maxwell system 363-01 · Nonuniqueness with local conservation for the hard-sphere Boltzmann equation 363-02 · Nonuniqueness for the periodic hard-sphere Boltzmann equation 364-01 · The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals 364-02 · Hard-sphere fluctuations on the regular Boltzmann lifespan 365-01 · Determination of a metric and a unitary connection from one boundary patch 365-02 · Smooth anisotropic uniqueness in the Calderón problem from one boundary patch 365-03 · Nonuniqueness for bounded measurable scalar conductivities in three dimensions 366-01 · Interior regularity of planar Mumford–Shah minimizers 367-01 · The critical dimension for one-phase Bernoulli minimizers 368-01 · Strong diffeomorphic approximation in three dimensions for 1≤p≤2 368-02 · Strong diffeomorphic approximation in three dimensions for p>2 369-01 · Strict hot spots and absence of interior critical points on smooth simply connected planar domains 370-01 · The Subcritical Hénon–Lane–Emden Conjecture 371-01 · Stable self-similar blowup for a supercritical defocusing Schrödinger equation on the torus 372-01 · Global Uniqueness for the Smooth Isotropic Elasticity Inverse Problem 373-01 · A counterexample to the Monge ansatz for the three-marginal Coulomb cost 374-01 · Sharp One-Third Stability of Brenier Maps 375-01 · A positive resolution of De Giorgi's conjecture in dimension eight 376-01 · Finite Instructions and Solenoidal Shear Flows 376-02 · A Fixed Particle Test for Computation in a Forced Viscous Flow 376-03 · Universal Computation with Eventually Stationary Navier–Stokes Forcing 376-04 · Geometric Programs for Solenoidal Forcing 376-05 · Prefix Instructions and Incompressible Flows 376-06 · Computation under Rapidly Vanishing Navier–Stokes Forcing 376-07 · Velocity-Field Detection of Computation in Forced Navier–Stokes Flows 376-08 · Scalar Potentials and Slow Clocks for Forced Fluid Computation 376-09 · Incompressible Box Transport and Finite Computation 377-01 · Uniform Interior C^{1,\alpha} Estimates for Infinity-Harmonic Functions w-001 · Algebraicity of Kuga Satake Correspondences for K3 Surfaces w-002 · Algebraicity of Weil classes on split abelian eightfolds w-003 · The rational Hodge conjecture for products of K3 surfaces e-001 · A pointwise 2 converse for elliptic curves with rational two torsion e-002 · Abelian covers Gale correspondences and the Hodge conjecture for powers e-003 · Conditional good minimal models for compact Kahler fourfolds e-004 · Deforming hypersymplectic four manifolds to hyperkahler triples e-005 · Exact Birch Swinnerton Dyer Formula from Low Selmer Corank e-006 · Finite ordinary minimal model programs on compact Kahler fourfolds e-007 · Fontaine Mazur modularity at the prime 2 e-008 · Gaussian free field limits of weighted integer Lipschitz heights e-009 · Goldfelds analytic density conjecture and the 2 converse for elliptic curves e-010 · Hilberts tenth problem over the rational numbers e-011 · Incompressible Box Transport and Finite Computation e-012 · Log abundance for compact Kahler spaces under logarithmic Iitaka subadditivity e-013 · Milnes rationality conjecture for abelian varieties e-014 · Numerical semiampleness of nef adjoint classes on compact Kahler manifolds e-015 · Taming implies compatibility on four manifolds e-016 · Termination of generalized canonical flips on compact Kahler fourfolds e-017 · Termination of generalized log canonical flips on compact Kahler fourfolds e-018 · The Gaussian free field limit of integer Lipschitz heights with two arc boundary data e-019 · The Selmer converse for elliptic curves at every prime e-020 · The joint scaling limit of critical Ashkin Teller currents e-021 · The mean analytic rank of quadratic twists of elliptic curves e-022 · The p adic section conjecture e-023 · The rational Hodge conjecture for CM abelian varieties e-024 · The two primary Birch Swinnerton Dyer formula in Selmer corank at most one e-025 · Uniform real Lipschitz surfaces on the triangular lattice e-026 · Unrestricted pro modularity at the prime two e-027 · Weil classes and Hodge classes on abelian powers OpenAI · 048-01 · 2026-09-23 · Algebraic and complex geometry
A singular normal affine surface with free tangent sheaf preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026
Family 048. A characteristic-zero counterexample to Lipman–Zariski.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems Standing problems . No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Constructs a singular normal affine complex surface with free rank-two tangent sheaf, disproving the characteristic-zero Lipman–Zariski conjecture.
We construct a singular normal affine complex surface whose tangent sheaf is free of rank two. This disproves the Lipman–Zariski conjecture in characteristic zero.
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.
A searchable companion, not a proof checker. A restatement is not a verification, and results from one manuscript are not results of another. The registered manuscripts were produced by Ngo Cheung. The OpenAI section is a separate catalogue by OpenAI and is not a theorem of that series. Cite one registered manuscript as Cheung, N., with its identifier, at enter.grok.me .