OpenAI Math·372 results·17 subjects
OpenAI's maths results, explained
In September and October 2026 OpenAI published a catalogue of 372 mathematical results it says its AI proved, from the Birch and Swinnerton-Dyer conjecture to the crossing number of complete graphs. Every result has a page here: what the problem asks, what OpenAI claims, the preprints, and the 3D animation once it is out. 35 results have a video so far and 1 have a full write-up.
These are preprints, not peer-reviewed publications. We explain the claims; we don't certify them.
By subject
Theoretical computer science
40 results · 1 with a video
Browse →Combinatorics
37 results · 7 with a video
Browse →Algebraic and complex geometry
36 results
Browse →Number theory
31 results · 8 with a video
Browse →Differential geometry
29 results · 3 with a video
Browse →Probability and statistical mechanics
29 results · 4 with a video
Browse →Mathematical physics
25 results · 3 with a video
Browse →Operator algebras
19 results
Browse →Algebra
18 results
Browse →Topology
18 results · 1 with a video
Browse →Partial differential equations
16 results · 2 with a video
Browse →Real and complex analysis
16 results · 3 with a video
Browse →Convex and metric geometry
15 results · 1 with a video
Browse →Group theory
14 results
Browse →Dynamical systems and ergodic theory
12 results · 2 with a video
Browse →Functional analysis
11 results
Browse →Mathematical logic
6 results
Browse →
Write-ups
Plain-English explanations of the results we have covered in depth: the problem, its history, what OpenAI claims and what is still unchecked.
Theoretical computer science 40
- 102The Unique Games Conjecture and optimal approximation thresholdsLean
- 103Exact derandomization of logarithmic space: L=RL=BPLLean
- 104Quasipolynomial algorithms for mean-payoff, stochastic and parity gamesLean
- 105Perfect completeness for 2-to-1 gamesLean
- 106Hardness of coloring three-colorable graphsLean
- 107Matrix multiplication with exponent at most 9/4Lean
- 108A cubic permanent–determinant lower boundLean
- 109Integer multiplication below n log n
- 110Optimal-order randomized k-server on arbitrary metricsLean
- 111One-sample matroid prophet inequalities against an almighty adversaryLean
- 112Beyond the square-root exponent for depth-three circuitsLean
- 113Approximate counting and entropy of perfect matchingsLean
- 114Approximate counting of common integer polymatroid basesLean
- 115Sampling and counting contingency tables with arbitrary marginsLean
- 116Uniform black-box noncommutative identity testing across characteristicsLean
- 117Uniform sparsest cut: hardness and semidefinite gapsLean
- 118Bin packing and unbounded configuration-LP gapsLean
- 119The Courtade–Kumar and Hellinger conjecturesLean
- 120Almost-linear-time exact matching and prescribed-degree factors in general graphs
- 121Almost-linear approximation of edit distanceLean
- 122Quantitative trace-reconstruction bounds with a uniform decoderLean
- 124Polynomial-time scheduling on three identical machinesLean
- 125The metric k-median approximation threshold and recoveryLean
- 126Exponential semidefinite complexity of perfect matchingLean
- 127Average sensitivity of polynomial threshold functionsVideoLean
- 128A factor-two approximation for shortest common superstringLean
- 129Exponential state costs for two-way automataLean
- 130Exact Fourier transforms below n log nLean
- 131Rapid mixing of graph switches for every degree sequenceLean
- 132A superquadratic separation of sensitivity and block sensitivityLean
- 133The computational complexity of Weisfeiler–Leman refinementLean
- 134Generalized star height at most threeLean
- 135Homogeneous depth-five lower bounds for iterated matrix multiplicationLean
- 136A quasilinear PCP theorem for PPAD
- 137One-tape time simulation in two-fifths-power spaceLean
- 138Subset Sum in O(20.49n) time
- 139Subpolynomial query complexity for log-concave samplingLean
- 140Memory–sample lower bounds for noiseless Gaussian regressionLean
- 141Existential–universal real sentences in the counting hierarchy
- 142Deterministic polynomial factorization over prime fields
Combinatorics 37
- 155A counterexample to periodic tiling in dimension threeLean
- 156Borsuk's conjecture fails in dimension nineLean
- 157Graph coloring, clique minors, and Colin de Verdière invariantsLean
- 158The Euclidean plane cannot be colored with five colorsVideoLean
- 159Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi boundsVideoLean
- 160Superexponential van der Waerden numbersLean
- 161Counterexamples to Sidorenko’s conjecture and the forcing conjectureLean
- 162Counterexamples to Ryser’s covering conjectureLean
- 164Hindman’s finite sums and products conjecture
- 165The Harary–Hill and Zarankiewicz crossing-number formulasWrite-upVideoLean
- 166The higher-dimensional Erdős distinct-distances conjecture
- 167Planar distinct distances and unit-distance boundsLean
- 168Combinatorial invariance of Kazhdan–Lusztig polynomialsLean
- 169Shareshian–Wachs elementary positivityLean
- 170Sharp logarithmic exponents for off-diagonal Ramsey numbersVideoLean
- 171The hypercube Ramsey conjectureVideo
- 172Classification of finite Euclidean Ramsey configurationsLean
- 173Seymour’s second-neighborhood conjectureLean
- 174Deterministic construction of strong thin spanning treesLean
- 175Talagrand’s expectation thresholds, discrete convexity, and graph decompositionsLean
- 176The second Kahn–Kalai conjecture with an edge-count boundLean
- 177Bounded-degree coboundary expandersLean
- 178Deterministic nonbipartite Ramanujan graphs in every fixed degree
- 179The circulant Hadamard and Barker-sequence conjecturesLean
- 180Barnette’s Hamiltonian-cycle conjectureVideoLean
- 181The Erdős–Gallai cycle-decomposition conjectureVideoLean
- 182Power savings for intersective polynomial differences and prime argumentsLean
- 183Power savings for planar halving lines and k-setsLean
- 184Correspondence coloring with a fixed forbidden subgraphLean
- 185Counterexamples to infinite matroid intersection and packing/coveringLean
- 186Uniform influence and sharp thresholds for graph and hypergraph propertiesLean
- 187Snaky in 21 Maker movesLean
- 188The sharp terminal leave in random triangle removalLean
- 189Cycle–clique Ramsey numbersLean
- 190Polynomial removal fails for ordered binary matricesLean
- 191A power improvement in the Heilbronn triangle lower boundLean
- 192Boolean functions violate the square-root degree bound by arbitrary factorsLean
Algebraic and complex geometry 36
- 032The rational Hodge conjecture for CM abelian varieties
- 033Iitaka subadditivity, variation, and logarithmic additivityLean
- 034Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity
- 035Log-canonical threefold abundance in numerical dimension one
- 036Numerical semiampleness and generalized minimal models
- 037The ordinary-double-point volume gap
- 038Fujita’s freeness conjecture
- 039Nagata’s conjecture and maximal Seshadri constantsLean
- 040Bloch’s conjecture for complex surfaces
- 041Hyperkähler SYZ and projective-space bases
- 042Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII
- 043P = W for fixed-determinant SLn moduli spaces
- 044The equivariant cohomological Hikita conjecture
- 046Shafarevich counterexamples in dimension two and with large fundamental group
- 047Zariski cancellation and affine fibrations over the complex numbersLean
- 048A characteristic-zero counterexample to Lipman–Zariski
- 049A stable-coordinate counterexample in four variablesLean
- 050A counterexample to Griffiths’ positivity conjectureLean
- 051Kobayashi’s canonical-ampleness conjecture
- 052Tangent splittings and product decompositionsLean
- 053A counterexample to Pixton completeness in Chow
- 054Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations
- 055Gepner symmetry and large-volume stability on threefolds
- 056Termination of projective and Kähler fourfold minimal model programs
- 057Fundamental groups of special complex varieties and root orbifolds
- 058Semialgebraic universal covers and bounded domainsLean
- 059Counterexamples to Zariski’s multiplicity conjecture
- 060The Global Spherical Shell conjecture
- 062Projective contact classification and the LeBrun–Salamon conjecture
- 063The generalized Mukai conjecture
- 064Topological triviality of μ-constant surface singularities
- 065Virasoro constraints for complete intersections and projective-bundle towers
- 066Bounded klt complements for Fano contractionsLean
- 067The Campana–Peternell conjecture in dimension six
- 068Anticanonical nonvanishing in every dimension
- 069Global quantum geometric Langlands at irrational level
Number theory 31
- 001Milne’s rationality conjecture and algebraic specializationVideo
- 002The full BSD formula from low Selmer corankVideo
- 003The quasi-Riemann hypothesisVideoLean
- 004Hilbert’s tenth problem over ℚVideo
- 005Irrationality of Catalan’s constantVideoLean
- 006Goldfeld’s conjecture: densities and mean analytic rankVideo
- 007Ordinary two-point correlations and the corrected Elliott conjectureLean
- 008The Deligne–Drinfeld conjectureLean
- 009Function-field reconstruction from Milnor K-theory and Galois dataLean
- 010Unrestricted pro-modularity at the prime two
- 011Prime-factor statistics of p-1Video
- 012Independent largest prime factors of consecutive integersLean
- 013Ostmann’s inverse Goldbach conjectureLean
- 014Restricted geometric Langlands, global Arthur enhancements, and generic RamanujanVideo
- 015Torus-packet equidistribution in prime, quartic, and sextic degreesLean
- 016Zilber–Pink in abelian varieties and the Siegel threefold
- 017The irrationality exponent of π is 2Lean
- 018The Margulis–Platonov conjecture over global fields
- 019The local p-adic section conjecture and global consequences
- 020Squarefree quartics and power-free polynomial valuesLean
- 021A quadratic bound for Jacobsthal’s functionLean
- 022The weak inhomogeneous Duffin–Schaeffer conjecture
- 023Patterson's first moment for cubic Gauss sumsLean
- 024An asymptotic formula for the number of totientsLean
- 025Short Egyptian fractionsLean
- 026Positive lower density of large prime gapsLean
- 027Potential integral density on curve character varietiesLean
- 028Uniformly bounded components of Gaussian-prime graphsLean
- 029Primitive roots for every admissible integer base
- 030Modularity of elliptic curves over imaginary quadratic fields
- 031Uchida’s conjecture for open homomorphisms of Galois groups
Differential geometry 29
- 333Smooth isometric immersions of surfaces into ℝ4Lean
- 334A smooth surface metric with no local isometric immersion in ℝ3Lean
- 335Gromov’s integral scalar-curvature bound for simplicial volume
- 336Spectral scalar curvature, Urysohn width, and macroscopic dimension
- 337Sharp Cartan–Hadamard isoperimetry and rigidityLean
- 338Yau's uniformization conjecture
- 339Katok's entropy rigidity conjecture
- 340A counterexample to the nearby Lagrangian conjecture
- 341Donaldson's hypersymplectic deformation conjecture
- 342Donaldson's tamed-to-compatible conjectureLean
- 343Symplectic ball packing in higher dimensionsLean
- 344The metric Blaschke conjecture
- 345Infinitely many closed geodesics on Riemannian spheres and closed three-manifoldsVideo
- 346Sharp singular-set bounds for stationary integral varifolds
- 347Counterexamples to stable-Morse and strong Arnold fixed-point boundsLean
- 348Nonnegative-curvature Einstein classification and an L2 topological gapLean
- 349The Solomon–Yau least-volume conjecture
- 350Yau’s nodal bounds: surfaces and higher dimensionsVideoLean
- 351Scalar curvature and finite-time Ricci-flow singularities
- 352A finite-time singularity of Calabi flow
- 353Affine Bernstein rigidity through dimension nine and a smooth dimension-ten counterexampleLean
- 354The isoperimetric profile of the cubic three-torusVideoLean
- 355Unique tangent flows at the first surface singularity
- 356Gigli’s characterization of Alexandrov curvatureLean
- 357Bi-Lipschitz coordinates at every regular RCD point
- 358A three-manifold without conjugate points or nonpositive curvatureLean
- 359Negative Kähler curvature without bounded holomorphic coordinatesLean
- 360Weak MTW curvature gives convexity and regular optimal transportLean
- 361Failure of integer-degree harmonic dimension comparisonLean
Probability and statistical mechanics 29
- 211The geometric phase diagram, diffusion, and spectra of random planar mapsLean
- 212Planar first-passage geometry and the absence of bigeodesicsLean
- 213Critical percolation on every quasi-transitive graphVideoLean
- 214The Benjamini–Schramm nonuniqueness conjectureLean
- 215Canonical O(3) continuum limit and exact O(4) mass asymptoticsLean
- 216Critical and near-critical XY scaling and BKT universality
- 217The low-temperature Sherrington–Kirkpatrick fluctuation law
- 218Conformal universality for weakly interacting and random-bond Ising modelsLean
- 219GOE bulk universality for regular graphs with weak Anderson disorder
- 220Directional zero–one laws beyond iid environments and iid ballisticityLean
- 221The Mézard–Parisi formula for diluted spin glassesLean
- 222Perceptron free energies and microscopic jamming exponentsLean
- 223Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling
- 224Critical and quenched near-critical universality for Poisson–Voronoi percolation
- 225Gaussian free field limits throughout the balanced six-vertex regime
- 226The double-dimer loop ensemble converges to CLE4Video
- 227Critical SK autocorrelation processes and dynamics across the temperature transitionLean
- 228Continuum phase transitions for radial pair potentialsLean
- 229Exact three- and four-state reconstruction thresholds and four-state tree capacityLean
- 230Exact Hausdorff gauges for SLEVideoLean
- 231The free uniform spanning forest is a factor of IIDLean
- 232Gaussian fields and interfaces for triangular-lattice Lipschitz heights
- 233The joint critical Ashkin–Teller current limit
- 234All-temperature pressure of orthogonally invariant Ising spin glassesLean
- 235Limiting random SAT thresholds, sharp variance and computabilityLean
- 236The exact factor-of-IID threshold for free Ising spins on treesLean
- 237The three-quarter exponent for honeycomb self-avoiding walkVideoLean
- 238Optimal logarithmic mixing of the Thorp shuffleLean
- 239Sharp singularity rates for symmetric random sign matrices
Mathematical physics 25
- 260Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensionsLean
- 261Localization and delocalization in the Anderson modelVideoLean
- 262Sharp finite-matrix Lieb–Thirring inequalities and all equality casesLean
- 263The ionization and generalized ionization conjecturesLean
- 264Strong cosmic censorship near two-ended Kerr data
- 265Area laws and tensor networks for two-dimensional gapped systems
- 266Exactly three mutually unbiased bases in dimension sixLean
- 267Positive-temperature Bose–Einstein condensation and exact quantum depletionLean
- 268The spin-one Haldane gap
- 269Uniform Laughlin gap and stability under bounded scalar disorderLean
- 270Threshold and positive-energy bound states of the BFSS matrix model
- 271Bloch's law, its lattice correction, and the spherical magnetization lawVideoLean
- 272Entanglement without distillable secret keyLean
- 273The entropy photon-number inequalityLean
- 274Parity is not in QAC0Lean
- 275QMA-hardness of continuum Coulomb energyLean
- 276Classical capacity of generalized amplitude dampingLean
- 277Threshold repetition for entangled gamesLean
- 278Failure of Kohn–Sham ensemble representation
- 279Exact quantum factoring over a fixed finite gate setVideoLean
- 280Unitary vertex operator algebras and conformal netsLean
- 281QAOA attains the SK optimum in the thermodynamic-first limitLean
- 282From scale symmetry to local conformal symmetry in four-dimensional QFT
- 283Polynomial-time unitary synthesis from a Boolean oracle
- 284The optimal quartic separation between randomized and quantum queries
Operator algebras 19
- 285Counterexamples to Baum–Connes and Kadison–Kaplansky
- 286Rigidity and arithmetic of lattice von Neumann algebras
- 287Isomorphism of the free group factorsLean
- 288Kadison's similarity conjectureLean
- 289Strong Kadison–Kastler stability and its spatial boundariesLean
- 290Relative bicentralizers and modular spectral recoveryLean
- 291Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stabilityLean
- 292Kirchberg's 𝒪2 norm-ultrapower embedding problemLean
- 293Invariant projections, hyperinvariant subspaces, and transitive algebrasLean
- 294Kaplansky's quasitrace conjecture and failure of tensor-product stable finitenessLean
- 295The Kadison–Ringrose cohomology conjectureLean
- 296The generator problem for finite factorsLean
- 297A ZFC counterexample to Naimark's problemLean
- 298Two notions of free entropy differ even when both are finiteLean
- 299The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stabilityLean
- 300Approximation and quadratic strong-operator paving
- 301Trace cones and Razak–Jacelon stabilizationLean
- 302Radius of comparison equals half the mean dimension
- 303Weak pure infiniteness and Cuntz-algebra absorptionLean
Algebra 18
- 193Serre’s intersection-multiplicity conjecture
- 194Lech’s multiplicity conjectureLean
- 195A counterexample to the small Cohen–Macaulay module conjectureLean
- 196A counterexample to Kaplansky’s zero-divisor conjectureLean
- 197A torsion-free group algebra that is not directly finiteLean
- 198A counterexample to finitistic-dimension finitenessLean
- 199Counterexamples to Auslander–Reiten, Tachikawa and related homological conjecturesLean
- 200Eisenbud–Green–Harris and lex-plus-powers
- 201A counterexample to Kurosh’s division-ring problem
- 202The blockwise Alperin weight conjecture
- 203Donovan's conjecture over fields and complete mixed-characteristic DVRs
- 204Tensor saturation for even spin groups
- 205Saxl’s conjecture and universal tensor squaresLean
- 206Finite lattice representation and undecidabilityLean
- 207The ℓ¹-Bass conjecture for all discrete groupsLean
- 208Finite symmetric tensor categories and the Verlinde tower
- 209Integral counterexamples to Gersten’s conjecture
- 210Foulkes' conjecture for sixth powers and quadratic stabilizationLean
Topology 18
- 304The Hilbert–Smith conjecture in every dimensionVideo
- 305Four-dimensional disk embedding and Wall's conjecture
- 306The purely cosmetic surgery conjecture
- 307Failure of rational injectivity for maximal coarse assemblyLean
- 308Finite Smith–Toda complexes at every height
- 309The Kervaire invariant problem at the prime three
- 310Quillen's conjecture in rational homology
- 311The Hovey–Strickland and Chai conjectures
- 312The Grothendieck homotopy hypothesisLean
- 313Finite generation for the K(n)-local sphere
- 314Cyclic length and chromatic fixed-point loss
- 315The four-dimensional Singer conjecture
- 316Curtis’s conjecture
- 317Thomason model structures in all strict higher dimensionsLean
- 318Chromatic splitting: filtrations and counterexamples
- 319Counterexamples to finite generation at chromatic height two
- 320Nonhomeomorphic closed aspherical four-manifolds
- 321A counterexample to Wall's finite D(2) problem
Partial differential equations 16
- 362Global smoothness for relativistic Vlasov–MaxwellVideoLean
- 363Nonuniqueness with local conservation for the hard-sphere Boltzmann equationLean
- 364Kinetic limits and fluctuations over the Boltzmann lifespan
- 365Joint metric and connection recovery from one boundary patchLean
- 366The planar Mumford–Shah regularity conjecture and local weak-L4 gradient bounds
- 367The critical dimension for the one-phase Bernoulli problemLean
- 368The three-dimensional Ball–Evans approximation problem
- 369The hot spots conjecture for simply connected planar domainsLean
- 370The Lane–Emden and Hénon–Lane–Emden conjecturesLean
- 371Stable blowup for the defocusing Schrödinger equationLean
- 372Global uniqueness in smooth isotropic elasticityLean
- 373Nonattainment of the three-marginal Coulomb Monge problemLean
- 374Sharp one-third stability of Brenier mapsLean
- 375De Giorgi's conjecture in dimension eight
- 376Universal computation in forced Navier–Stokes flowsVideoLean
- 377Interior C1,α regularity for infinity-harmonic functions
Real and complex analysis 16
- 071Koebe’s circle-domain conjectureLean
- 072Brennan's conjecture and the integral-means spectrumLean
- 073The Falconer distance conjectureLean
- 074Kakeya in three and four dimensionsVideo
- 075The L log L Fourier-convergence conjectureVideoLean
- 076Real ultraflat Littlewood polynomials and unbounded binary merit factorsLean
- 077Fourier restriction for positively curved surfaces
- 078The three-dimensional Bochner–Riesz conjecture
- 079Local smoothing in three dimensions
- 080The exact Sobolev endpoint for Schrödinger convergence
- 081Riesz transforms and rectifiability in higher codimensionLean
- 082Annular variation and dyadic absolute bounds for the triangular Hilbert transformLean
- 083Hilbert transforms along Lipschitz directionsLean
- 084The geometric case of the Erdős similarity conjectureVideoLean
- 085Endpoint Sobolev regularity of centered disk averagesLean
- 086An L3 bound for the trilinear Hilbert transform
Convex and metric geometry 15
- 087The Mahler conjectures, functional inequalities and polar-product symplectic widthVideoLean
- 088Sharp projection-body inequalities and a counterexample to simplex maximizationLean
- 089Bounded-distortion L1 embeddings of planar and bounded-treewidth graphsLean
- 090Triangular-lattice optimality, long-range Riesz and Coulomb energies, and spherical logarithmic energyLean
- 091Logarithmic and Lp Brunn–Minkowski inequalities and the B-conjectureLean
- 092The optimal order of convex-body covering densityLean
- 093Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures
- 094Subpolynomial dimension reduction in LpLean
- 095Hyperbolicity cones without semidefinite liftsLean
- 096The Gaussian propeller conjecture in every dimensionLean
- 097The Euclidean Steinitz–Bergström boundLean
- 098Compact counterexamples to bi-Lipschitz dimension reductionLean
- 099The sharp exponential scale of edit-distance distortionLean
- 100Cylinder coverings below the half-area boundLean
- 101The sharp simplex conjecture for isotropic constants
Group theory 14
- 246Cannon's conjectureLean
- 247An infinite finitely presented residually finite 2-group and a finitely presented nil algebraLean
- 248Thompson's group F is nonamenableLean
- 249A finitely generated Eilenberg–Ganea counterexampleLean
- 250Boone–Higman embeddings with higher finitenessLean
- 251Amenability, unitarizability, and strong Ulam stabilityLean
- 252A torsion-free hyperbolic group that is neither residually finite nor linear over any fieldLean
- 253An infinite finitely presented simple amenable groupLean
- 254Classifying spaces and geometric obstructions for Artin groupsLean
- 255Quasi-isometric recognition of virtually polycyclic groupsLean
- 256Nonsingular systems of equations over arbitrary groupsLean
- 257A hyperbolic group without a geometric CAT(0) actionLean
- 258Gersten’s conjecture and virtual compact specialness of one-relator groups
- 259A group without fixed price
Dynamical systems and ergodic theory 12
- 143Hilbert's sixteenth problem: uniform bounds for limit cyclesVideoLean
- 144Banach’s simple Lebesgue-spectrum problemLean
- 145Rokhlin’s multiple-mixing problemLean
- 146Positive metric entropy for the standard mapLean
- 147The near-boundary Birkhoff conjecture
- 148The entropy-rate dimension formula for self-similar measuresLean
- 149Classwise permanence for weakly reversible mass-action systemsLean
- 150Weak mixing of triangular billiards with an irrational angleVideoLean
- 151A C1 counterexample to the entropy conjectureLean
- 152Zero entropy does not guarantee a smooth positive-volume modelLean
- 153Arithmetic classification and non-Pisot singularity for Bernoulli convolutions
- 154Pointwise multiple ergodic averages for mixing transformations
Functional analysis 11
- 322Tingley’s sphere-isometry problemLean
- 323Independence of the separable quotient problemLean
- 324Lipschitz equivalent Banach spaces need not be linearly isomorphicLean
- 325The complete Crouzeix conjectureLean
- 326The cotype–cotype conjecture under the approximation propertyLean
- 327Markov type characterizes superreflexivityLean
- 328Nonexpansive fixed points in reflexive Banach spacesLean
- 329A counterexample to metric-entropy dualityLean
- 330A uniformly discrete counterexample to bounded approximation in Lipschitz-free spacesLean
- 331Reflexive midpoint convexity and diamond distortionLean
- 332Metric Markov cotype of ℓ1 and Hilbert-space Lipschitz extension
Mathematical logic 6
- 240Shelah's eventual categoricity and the prescribed-threshold obstructionLean
- 241Rigidity of the Turing degreesLean
- 242Single-fold Diophantine representations and undecidability under an at-most-one-solution promiseLean
- 243Separating choiceless counting from polynomial time and witnessed choiceLean
- 244The Partition Principle does not imply ChoiceLean
- 245Weak normalization implies strong normalization in pure type systemsLean