# Claimed, not yet checked

> 130 AI-made math results: claimed, not yet checked, each explained in plain English. These results are claimed in a paper but no formal proof is listed…

Canonical: https://closedform.nishachay.tech/trust/claimed/
Last updated: 2026-10-14

These results are claimed in a paper but no formal proof is listed, so they rest on the written argument until experts or a proof checker confirm them.

130 AI-made results with this trust label, from 244 papers in the OpenAI math collection, each explained in plain English. None has a formal proof listed yet; all are claimed in a paper. They span 16 fields, led by algebraic and complex geometry (28), topology (15) and differential geometry (14). The oldest question here dates back to 1902: [The Hilbert–Smith conjecture in every dimension](https://closedform.nishachay.tech/e/openai-math-2026-304/). Results rated Landmark include [The full BSD formula from low Selmer corank](https://closedform.nishachay.tech/e/openai-math-2026-002/) and [Hilbert’s tenth problem over ℚ](https://closedform.nishachay.tech/e/openai-math-2026-004/).

## Results (130)

- [Milne’s rationality conjecture and algebraic specialization](https://closedform.nishachay.tech/e/openai-math-2026-001/) - Entry 001 · After reduction mod p, Hodge classes on abelian varieties are claimed to give one rational number in every cohomology. (Claimed, not checked)
- [The full BSD formula from low Selmer corank](https://closedform.nishachay.tech/e/openai-math-2026-002/) - Entry 002 · The full Birch–Swinnerton-Dyer formula is claimed for every elliptic curve with a small Selmer group at one prime. (Claimed, not checked)
- [Hilbert’s tenth problem over ℚ](https://closedform.nishachay.tech/e/openai-math-2026-004/) - Entry 004 · No algorithm can decide whether a whole-number polynomial equation has a solution in fractions, the paper claims. (Claimed, not checked)
- [Goldfeld’s conjecture: densities and mean analytic rank](https://closedform.nishachay.tech/e/openai-math-2026-006/) - Entry 006 · Among the quadratic twists of any elliptic curve, half are claimed to have analytic rank 0 and half rank 1. (Claimed, not checked)
- [Unrestricted pro-modularity at the prime two](https://closedform.nishachay.tech/e/openai-math-2026-010/) - Entry 010 · Odd two-dimensional 2-adic Galois representations are claimed to come from modular forms, with no condition mod 2. (Claimed, not checked)
- [Prime-factor statistics of p-1](https://closedform.nishachay.tech/e/openai-math-2026-011/) - Entry 011 · The prime factors of p − 1, for a random prime p, are claimed to split like a randomly broken stick. (Claimed, not checked)
- [Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan](https://closedform.nishachay.tech/e/openai-math-2026-014/) - Entry 014 · Linked papers claim the restricted geometric Langlands equivalence in characteristic p, plus Ramanujan bounds. (Claimed, not checked)
- [Zilber–Pink in abelian varieties and the Siegel threefold](https://closedform.nishachay.tech/e/openai-math-2026-016/) - Entry 016 · Unlikely intersections in abelian varieties are claimed to be finite in number, in every dimension. (Claimed, not checked)
- [The Margulis–Platonov conjecture over global fields](https://closedform.nishachay.tech/e/openai-math-2026-018/) - Entry 018 · Normal subgroups of these simple groups over any global field are claimed to come from finitely many local pieces. (Claimed, not checked)
- [The local p -adic section conjecture and global consequences](https://closedform.nishachay.tech/e/openai-math-2026-019/) - Entry 019 · Points on p-adic curves of genus two or more are claimed to match exactly the sections of their fundamental group. (Claimed, not checked)
- [The weak inhomogeneous Duffin–Schaeffer conjecture](https://closedform.nishachay.tech/e/openai-math-2026-022/) - Entry 022 · For any fixed shift, a weighted sum decides whether almost every number is well approximated. (Claimed, not checked)
- [Primitive roots for every admissible integer base](https://closedform.nishachay.tech/e/openai-math-2026-029/) - Entry 029 · Every whole number except −1 and perfect squares is claimed to be a primitive root for infinitely many primes. (Claimed, not checked)
- [Modularity of elliptic curves over imaginary quadratic fields](https://closedform.nishachay.tech/e/openai-math-2026-030/) - Entry 030 · Every elliptic curve over every imaginary quadratic field is claimed to match an automorphic form, place by place. (Claimed, not checked)
- [Uchida’s conjecture for open homomorphisms of Galois groups](https://closedform.nishachay.tech/e/openai-math-2026-031/) - Entry 031 · Every open map between these Galois groups is claimed to come from a unique map between the fields. (Claimed, not checked)
- [The rational Hodge conjecture for CM abelian varieties](https://closedform.nishachay.tech/e/openai-math-2026-032/) - Entry 032 · The rational Hodge conjecture is claimed for every abelian variety with complex multiplication, in every dimension. (Claimed, not checked)
- [Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity](https://closedform.nishachay.tech/e/openai-math-2026-034/) - Entry 034 · A family of 14 papers claims log abundance in characteristic zero and the effective Iitaka fibration conjecture. (Claimed, not checked)
- [Log-canonical threefold abundance in numerical dimension one](https://closedform.nishachay.tech/e/openai-math-2026-035/) - Entry 035 · In characteristic above 3, a nef log canonical threefold divisor of numerical dimension one is claimed to give a map. (Claimed, not checked)
- [Numerical semiampleness and generalized minimal models](https://closedform.nishachay.tech/e/openai-math-2026-036/) - Entry 036 · Nef adjoint divisors with an extra nef part are claimed to be numerically semiample; minimal models are claimed too. (Claimed, not checked)
- [The ordinary-double-point volume gap](https://closedform.nishachay.tech/e/openai-math-2026-037/) - Entry 037 · Every singular point of a mild kind is at most as roomy as a double cone, in any dimension. (Claimed, not checked)
- [Fujita’s freeness conjecture](https://closedform.nishachay.tech/e/openai-math-2026-038/) - Entry 038 · On every smooth shape, n + 1 copies of a positive bundle are always enough for Fujita's freeness. (Claimed, not checked)
- [Bloch’s conjecture for complex surfaces](https://closedform.nishachay.tech/e/openai-math-2026-040/) - Entry 040 · On a complex surface with no holomorphic two-forms, zero-cycles carry only their degree and Albanese data. (Claimed, not checked)
- [Hyperkähler SYZ and projective-space bases](https://closedform.nishachay.tech/e/openai-math-2026-041/) - Entry 041 · Every nonzero nef isotropic line bundle on a compact hyperkähler manifold is claimed to give a torus fibration. (Claimed, not checked)
- [Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII](https://closedform.nishachay.tech/e/openai-math-2026-042/) - Entry 042 · A claimed proof that every complex K3 surface is Oka: local holomorphic maps into it can be copied by entire maps. (Claimed, not checked)
- [P = W for fixed-determinant SL n moduli spaces](https://closedform.nishachay.tech/e/openai-math-2026-043/) - Entry 043 · Two ways of layering the cohomology of SL_n Higgs moduli are claimed to agree in every composite coprime rank. (Claimed, not checked)
- [The equivariant cohomological Hikita conjecture](https://closedform.nishachay.tech/e/openai-math-2026-044/) - Entry 044 · For every finite quiver, the cohomology of a Nakajima variety is claimed to equal functions on a Coulomb fixed scheme. (Claimed, not checked)
- [Shafarevich counterexamples in dimension two and with large fundamental group](https://closedform.nishachay.tech/e/openai-math-2026-046/) - Entry 046 · Two claimed counterexamples to Shafarevich's conjecture: a surface and a fourfold whose universal covers fail convexity. (Claimed, not checked)
- [A characteristic-zero counterexample to Lipman–Zariski](https://closedform.nishachay.tech/e/openai-math-2026-048/) - Entry 048 · A singular complex surface whose vector fields still form a free basis, against the Lipman–Zariski conjecture. (Claimed, not checked)
- [Kobayashi’s canonical-ampleness conjecture](https://closedform.nishachay.tech/e/openai-math-2026-051/) - Entry 051 · Compact Kähler manifolds with no entire curves have ample canonical bundle, as Kobayashi conjectured. (Claimed, not checked)
- [A counterexample to Pixton completeness in Chow](https://closedform.nishachay.tech/e/openai-math-2026-053/) - Entry 053 · A tautological relation in genus 10^60 that Pixton’s original relations miss, in Chow and in cohomology. (Claimed, not checked)
- [Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations](https://closedform.nishachay.tech/e/openai-math-2026-054/) - Entry 054 · Very general cubic fourfolds of large admissible discriminant are irrational despite a K3 derived category. (Claimed, not checked)
- [Gepner symmetry and large-volume stability on threefolds](https://closedform.nishachay.tech/e/openai-math-2026-055/) - Entry 055 · A stability condition on every smooth quintic threefold with Toda’s exact 2/5 Gepner symmetry. (Claimed, not checked)
- [Termination of projective and Kähler fourfold minimal model programs](https://closedform.nishachay.tech/e/openai-math-2026-056/) - Entry 056 · Every permitted minimal model program on a projective log canonical fourfold claims to stop after finitely many steps. (Claimed, not checked)
- [Fundamental groups of special complex varieties and root orbifolds](https://closedform.nishachay.tech/e/openai-math-2026-057/) - Entry 057 · Special compact Kähler manifolds claim virtually abelian fundamental groups in every dimension, as Campana predicted. (Claimed, not checked)
- [Counterexamples to Zariski’s multiplicity conjecture](https://closedform.nishachay.tech/e/openai-math-2026-059/) - Entry 059 · Two hypersurface germs with the same embedded topology but different multiplicities, against Zariski’s 1971 question. (Claimed, not checked)
- [The Global Spherical Shell conjecture](https://closedform.nishachay.tech/e/openai-math-2026-060/) - Entry 060 · Every minimal class VII surface with positive second Betti number contains a global spherical shell. (Claimed, not checked)
- [Projective contact classification and the LeBrun–Salamon conjecture](https://closedform.nishachay.tech/e/openai-math-2026-062/) - Entry 062 · Contact Fano manifolds are homogeneous, which settles the LeBrun–Salamon conjecture on quaternionic-Kähler spaces. (Claimed, not checked)
- [The generalized Mukai conjecture](https://closedform.nishachay.tech/e/openai-math-2026-063/) - Entry 063 · A claimed proof that rational curves on a Fano manifold cap its Picard number, with equality only for product spaces. (Claimed, not checked)
- [Topological triviality of μ -constant surface singularities](https://closedform.nishachay.tech/e/openai-math-2026-064/) - Entry 064 · A claimed proof that surface singularities with a constant Milnor number keep the same topology along a family. (Claimed, not checked)
- [Virasoro constraints for complete intersections and projective-bundle towers](https://closedform.nishachay.tech/e/openai-math-2026-065/) - Entry 065 · Claimed proofs that curve counts on complete intersections and on projective bundles obey the Virasoro equations. (Claimed, not checked)
- [The Campana–Peternell conjecture in dimension six](https://closedform.nishachay.tech/e/openai-math-2026-067/) - Entry 067 · A claimed proof that every six-dimensional Fano manifold with nef tangent bundle is a symmetric, homogeneous space. (Claimed, not checked)
- [Anticanonical nonvanishing in every dimension](https://closedform.nishachay.tech/e/openai-math-2026-068/) - Entry 068 · A claimed proof that a smooth nonnegatively curved anticanonical bundle always has a section of some power. (Claimed, not checked)
- [Global quantum geometric Langlands at irrational level](https://closedform.nishachay.tech/e/openai-math-2026-069/) - Entry 069 · A claimed proof of quantum geometric Langlands duality on any smooth complex curve at every irrational level. (Claimed, not checked)
- [Kakeya in three and four dimensions](https://closedform.nishachay.tech/e/openai-math-2026-074/) - Entry 074 · Claimed proofs: the Kakeya maximal conjecture in 3D, and full dimension for every Kakeya set in 4D. (Claimed, not checked)
- [Fourier restriction for positively curved surfaces](https://closedform.nishachay.tech/e/openai-math-2026-077/) - Entry 077 · Claimed proofs of the full Fourier restriction range p > 3 for the sphere and for positively curved surfaces. (Claimed, not checked)
- [The three-dimensional Bochner–Riesz conjecture](https://closedform.nishachay.tech/e/openai-math-2026-078/) - Entry 078 · A claimed proof of the Bochner–Riesz conjecture in three dimensions, in its strict-order form. (Claimed, not checked)
- [Local smoothing in three dimensions](https://closedform.nishachay.tech/e/openai-math-2026-079/) - Entry 079 · A claimed proof of Sogge's local smoothing conjecture for waves in 3D space, including the critical case p = 3. (Claimed, not checked)
- [The exact Sobolev endpoint for Schrödinger convergence](https://closedform.nishachay.tech/e/openai-math-2026-080/) - Entry 080 · Claimed proofs that Schrödinger waves return to rough data at the exact smoothness threshold, in dimensions n ≥ 2. (Claimed, not checked)
- [An L 3 bound for the trilinear Hilbert transform](https://closedform.nishachay.tech/e/openai-math-2026-086/) - Entry 086 · A singular average of three shifted functions obeys an L³ × L³ × L³ to L¹ size bound, the paper claims. (Claimed, not checked)
- [Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures](https://closedform.nishachay.tech/e/openai-math-2026-093/) - Entry 093 · Log-concave laws with bell-curve tails in every direction obey a dimension-free log-Sobolev bound, the paper claims. (Claimed, not checked)
- [The sharp simplex conjecture for isotropic constants](https://closedform.nishachay.tech/e/openai-math-2026-101/) - Entry 101 · In every dimension, simplices alone have the largest isotropic constant among convex bodies, the paper claims. (Claimed, not checked)
- [Integer multiplication below n log n](https://closedform.nishachay.tech/e/openai-math-2026-109/) - Entry 109 · A tape-based computer can multiply huge whole numbers slightly faster than the long-conjectured n log n limit. (Claimed, not checked)
- [Almost-linear-time exact matching and prescribed-degree factors in general graphs](https://closedform.nishachay.tech/e/openai-math-2026-120/) - Entry 120 · A randomized algorithm finds a largest matching in any graph in almost-linear time, the paper claims. (Claimed, not checked)
- [A quasilinear PCP theorem for PPAD](https://closedform.nishachay.tech/e/openai-math-2026-136/) - Entry 136 · End-of-Line puzzles turn into number circuits only slightly bigger that tolerate many broken gates, the paper claims. (Claimed, not checked)
- [Subset Sum in O(2^(0.49n)) time](https://closedform.nishachay.tech/e/openai-math-2026-138/) - Entry 138 · A randomized algorithm claims to decide every Subset Sum instance in O(2^(0.49n)) time, below the 2^(n/2) scale. (Claimed, not checked)
- [Existential–universal real sentences in the counting hierarchy](https://closedform.nishachay.tech/e/openai-math-2026-141/) - Entry 141 · Deciding “there is x so that for every y” questions about real numbers claimed at one fixed counting level. (Claimed, not checked)
- [Deterministic polynomial factorization over prime fields](https://closedform.nishachay.tech/e/openai-math-2026-142/) - Entry 142 · A claimed coin-free algorithm that factors any polynomial modulo a prime in time polynomial in the input size. (Claimed, not checked)
- [The near-boundary Birkhoff conjecture](https://closedform.nishachay.tech/e/openai-math-2026-147/) - Entry 147 · Two papers claim that a smooth billiard table with an unbroken band of caustics along its edge must be an ellipse. (Claimed, not checked)
- [Arithmetic classification and non-Pisot singularity for Bernoulli convolutions](https://closedform.nishachay.tech/e/openai-math-2026-153/) - Entry 153 · Claimed singular Bernoulli convolutions beyond Pisot reciprocals, plus an arithmetic test for every parameter. (Claimed, not checked)
- [Pointwise multiple ergodic averages for mixing transformations](https://closedform.nishachay.tech/e/openai-math-2026-154/) - Entry 154 · For mixing systems, averages along k, 2k, …, nk are claimed to settle at almost every starting point, for every n. (Claimed, not checked)
- [Hindman’s finite sums and products conjecture](https://closedform.nishachay.tech/e/openai-math-2026-164/) - Entry 164 · However whole numbers are colored, some set of each size has its sums and products in one color, the paper claims. (Claimed, not checked)
- [The higher-dimensional Erdős distinct-distances conjecture](https://closedform.nishachay.tech/e/openai-math-2026-166/) - Entry 166 · Any n points in d ≥ 3 dimensions span at least a constant times n^(2/d) distinct distances, the paper claims. (Claimed, not checked)
- [The hypercube Ramsey conjecture](https://closedform.nishachay.tech/e/openai-math-2026-171/) - Entry 171 · Two-coloring the links among a constant times 2ⁿ points always gives a one-color n-dimensional cube, the paper claims. (Claimed, not checked)
- [Deterministic nonbipartite Ramanujan graphs in every fixed degree](https://closedform.nishachay.tech/e/openai-math-2026-178/) - Entry 178 · A fixed recipe builds networks with best-possible mixing, in every degree and every large even size. (Claimed, not checked)
- [Serre’s intersection-multiplicity conjecture](https://closedform.nishachay.tech/e/openai-math-2026-193/) - Entry 193 · Serre's intersection multiplicity is claimed to be strictly positive over every regular local ring. (Claimed, not checked)
- [Eisenbud–Green–Harris and lex-plus-powers](https://closedform.nishachay.tech/e/openai-math-2026-200/) - Entry 200 · Two papers claim the Eisenbud–Green–Harris and lex-plus-powers conjectures over every field of characteristic zero. (Claimed, not checked)
- [A counterexample to Kurosh’s division-ring problem](https://closedform.nishachay.tech/e/openai-math-2026-201/) - Entry 201 · A division ring made from two elements, each element algebraic, can still be infinite-dimensional over its center. (Claimed, not checked)
- [The blockwise Alperin weight conjecture](https://closedform.nishachay.tech/e/openai-math-2026-202/) - Entry 202 · A paper claims to prove Alperin's weight conjecture, block by block, for every finite group and every prime. (Claimed, not checked)
- [Donovan's conjecture over fields and complete mixed-characteristic DVRs](https://closedform.nishachay.tech/e/openai-math-2026-203/) - Entry 203 · Two papers claim Donovan's conjecture: blocks with bounded defect fall into finitely many types, for every prime. (Claimed, not checked)
- [Tensor saturation for even spin groups](https://closedform.nishachay.tech/e/openai-math-2026-204/) - Entry 204 · For even spin groups, an invariant after stretching the weights implies one before, if the weights pass a parity test. (Claimed, not checked)
- [Finite symmetric tensor categories and the Verlinde tower](https://closedform.nishachay.tech/e/openai-math-2026-208/) - Entry 208 · Every finite symmetric tensor category in characteristic p is claimed to map into one higher Verlinde category. (Claimed, not checked)
- [Integral counterexamples to Gersten’s conjecture](https://closedform.nishachay.tech/e/openai-math-2026-209/) - Entry 209 · Two ramified rings are claimed to break Gersten's conjecture: nonzero K-theory classes vanish over their fractions. (Claimed, not checked)
- [Critical and near-critical XY scaling and BKT universality](https://closedform.nishachay.tech/e/openai-math-2026-216/) - Entry 216 · Six papers claim exact critical laws for the planar XY model, as the Berezinskii–Kosterlitz–Thouless picture predicts. (Claimed, not checked)
- [The low-temperature Sherrington–Kirkpatrick fluctuation law](https://closedform.nishachay.tech/e/openai-math-2026-217/) - Entry 217 · The typical spread of the low-temperature Sherrington–Kirkpatrick free energy grows like n^(1/6), with a limiting law. (Claimed, not checked)
- [GOE bulk universality for regular graphs with weak Anderson disorder](https://closedform.nishachay.tech/e/openai-math-2026-219/) - Entry 219 · Eigenvalue spacings of random regular graphs, even with weak random potentials, match those of Gaussian random matrices. (Claimed, not checked)
- [Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling](https://closedform.nishachay.tech/e/openai-math-2026-223/) - Entry 223 · Critical random-cluster interfaces on the square grid converge to SLE curves for every cluster weight up to 4. (Claimed, not checked)
- [Critical and quenched near-critical universality for Poisson–Voronoi percolation](https://closedform.nishachay.tech/e/openai-math-2026-224/) - Entry 224 · Cardy's formula holds for Poisson–Voronoi percolation, and near-critical thresholds match the triangular lattice. (Claimed, not checked)
- [Gaussian free field limits throughout the balanced six-vertex regime](https://closedform.nishachay.tech/e/openai-math-2026-225/) - Entry 225 · The balanced six-vertex height surface tends to a Gaussian free field for all c up to 2, with variance 1/arcsin(c/2). (Claimed, not checked)
- [The double-dimer loop ensemble converges to CLE 4](https://closedform.nishachay.tech/e/openai-math-2026-226/) - Entry 226 · Loops from two overlaid random domino tilings of the half-plane converge, as curves, to nested CLE₄. (Claimed, not checked)
- [Gaussian fields and interfaces for triangular-lattice Lipschitz heights](https://closedform.nishachay.tech/e/openai-math-2026-232/) - Entry 232 · Random Lipschitz height surfaces on the triangular lattice converge to the Gaussian free field. (Claimed, not checked)
- [The joint critical Ashkin–Teller current limit](https://closedform.nishachay.tech/e/openai-math-2026-233/) - Entry 233 · Heights and current clusters of the critical Ashkin–Teller model converge together to a free field and its local sets. (Claimed, not checked)
- [Sharp singularity rates for symmetric random sign matrices](https://closedform.nishachay.tech/e/openai-math-2026-239/) - Entry 239 · Claims a random symmetric ±1 matrix is singular with probability (1/2 + o(1))ⁿ, with a matching biased-sign rate. (Claimed, not checked)
- [Gersten’s conjecture and virtual compact specialness of one-relator groups](https://closedform.nishachay.tech/e/openai-math-2026-258/) - Entry 258 · Claims one-relator groups without Baumslag–Solitar subgroups are hyperbolic and virtually compact special. (Claimed, not checked)
- [A group without fixed price](https://closedform.nishachay.tech/e/openai-math-2026-259/) - Entry 259 · Claims a finitely generated group with two free measure-preserving actions of different costs, so fixed price fails. (Claimed, not checked)
- [Strong cosmic censorship near two-ended Kerr data](https://closedform.nishachay.tech/e/openai-math-2026-264/) - Entry 264 · Claims typical vacuum perturbations of a rotating Kerr black hole cannot be smoothly continued past the inner horizon. (Claimed, not checked)
- [Area laws and tensor networks for two-dimensional gapped systems](https://closedform.nishachay.tech/e/openai-math-2026-265/) - Entry 265 · Claims the 2D area law: gapped ground states on a square grid hold entanglement proportional to boundary, not volume. (Claimed, not checked)
- [The spin-one Haldane gap](https://closedform.nishachay.tech/e/openai-math-2026-268/) - Entry 268 · Claims the spin-one Haldane gap: the Heisenberg chain on even rings has an energy gap that stays above log(20)/784. (Claimed, not checked)
- [Threshold and positive-energy bound states of the BFSS matrix model](https://closedform.nishachay.tech/e/openai-math-2026-270/) - Entry 270 · Claims the BFSS matrix model has one zero-energy bound state for every N, and many positive-energy states at N = 2. (Claimed, not checked)
- [Failure of Kohn–Sham ensemble representation](https://closedform.nishachay.tech/e/openai-math-2026-278/) - Entry 278 · Claims a three-electron molecule whose ground-state density no Kohn–Sham ensemble can reproduce. (Claimed, not checked)
- [From scale symmetry to local conformal symmetry in four-dimensional QFT](https://closedform.nishachay.tech/e/openai-math-2026-282/) - Entry 282 · Claims that scale symmetry forces local conformal symmetry for a broad class of four-dimensional quantum field theories. (Claimed, not checked)
- [Polynomial-time unitary synthesis from a Boolean oracle](https://closedform.nishachay.tech/e/openai-math-2026-283/) - Entry 283 · Claims a polynomial-size quantum circuit can carry out any n-qubit operation, given a suitable Boolean oracle. (Claimed, not checked)
- [The optimal quartic separation between randomized and quantum queries](https://closedform.nishachay.tech/e/openai-math-2026-284/) - Entry 284 · Claims functions where randomized queries need nearly the fourth power of quantum queries, refuting a cubic conjecture. (Claimed, not checked)
- [Counterexamples to Baum–Connes and Kadison–Kaplansky](https://closedform.nishachay.tech/e/openai-math-2026-285/) - Entry 285 · Claims torsion-free groups that break the Kadison–Kaplansky projection conjecture and reduced Baum–Connes. (Claimed, not checked)
- [Rigidity and arithmetic of lattice von Neumann algebras](https://closedform.nishachay.tech/e/openai-math-2026-286/) - Entry 286 · Claims the von Neumann algebra of a property (T) lattice remembers its group, its twist and its scale. (Claimed, not checked)
- [Approximation and quadratic strong-operator paving](https://closedform.nishachay.tech/e/openai-math-2026-300/) - Entry 300 · Claims to settle both paving conjectures of Popa and Vaes for every maximal abelian subalgebra of a von Neumann algebra. (Claimed, not checked)
- [Radius of comparison equals half the mean dimension](https://closedform.nishachay.tech/e/openai-math-2026-302/) - Entry 302 · Claims the radius of comparison of a minimal crossed product is half the mean dimension, the Phillips–Toms conjecture. (Claimed, not checked)
- [The Hilbert–Smith conjecture in every dimension](https://closedform.nishachay.tech/e/openai-math-2026-304/) - Entry 304 · Claims a proof of Hilbert–Smith: a locally compact group acting faithfully on a connected manifold is a Lie group. (Claimed, not checked)
- [Four-dimensional disk embedding and Wall's conjecture](https://closedform.nishachay.tech/e/openai-math-2026-305/) - Entry 305 · Claims the two-generator free group is not good for 4D surgery, plus a counterexample to Wall's question. (Claimed, not checked)
- [The purely cosmetic surgery conjecture](https://closedform.nishachay.tech/e/openai-math-2026-306/) - Entry 306 · Claims that two different surgeries on a nontrivial knot never give the same oriented three-dimensional space. (Claimed, not checked)
- [Finite Smith–Toda complexes at every height](https://closedform.nishachay.tech/e/openai-math-2026-308/) - Entry 308 · Claims Smith–Toda complexes exist at every height if the prime may grow, with an explicit V(4) at the prime 1009. (Claimed, not checked)
- [The Kervaire invariant problem at the prime three](https://closedform.nishachay.tech/e/openai-math-2026-309/) - Entry 309 · Claims to settle which odd-primary Kervaire classes survive at the prime three: stems 10, 106 and 322. (Claimed, not checked)
- [Quillen's conjecture in rational homology](https://closedform.nishachay.tech/e/openai-math-2026-310/) - Entry 310 · Claims Quillen's 1978 conjecture on subgroup posets for every finite group and every prime, in a stronger homology form. (Claimed, not checked)
- [The Hovey–Strickland and Chai conjectures](https://closedform.nishachay.tech/e/openai-math-2026-311/) - Entry 311 · Claims Chai's invariant-ideal conjecture at every prime and height, and with it the Hovey–Strickland classification. (Claimed, not checked)
- [Finite generation for the K(n)-local sphere](https://closedform.nishachay.tech/e/openai-math-2026-313/) - Entry 313 · Claims every homotopy group of the K(n)-local sphere is finitely generated over the p-adic integers. (Claimed, not checked)
- [Cyclic length and chromatic fixed-point loss](https://closedform.nishachay.tech/e/openai-math-2026-314/) - Entry 314 · Claims the exact chromatic loss between fixed points of p-group actions is a count of cyclic steps. (Claimed, not checked)
- [The four-dimensional Singer conjecture](https://closedform.nishachay.tech/e/openai-math-2026-315/) - Entry 315 · Claims the Singer conjecture in dimension four: L²-Betti numbers of aspherical four-manifolds vanish off degree two. (Claimed, not checked)
- [Curtis’s conjecture](https://closedform.nishachay.tech/e/openai-math-2026-316/) - Entry 316 · A paper claims to prove Curtis's 1975 conjecture: only η, ν, σ and Kervaire classes show up in mod-2 sphere homology. (Claimed, not checked)
- [Chromatic splitting: filtrations and counterexamples](https://closedform.nishachay.tech/e/openai-math-2026-318/) - Entry 318 · Five papers claim Hopkins' chromatic splitting conjecture fails in its strong and weak forms, and offer a filtered fix. (Claimed, not checked)
- [Counterexamples to finite generation at chromatic height two](https://closedform.nishachay.tech/e/openai-math-2026-319/) - Entry 319 · A paper claims to disprove the Hahn–Wilson conjecture at height two, for every large enough prime. (Claimed, not checked)
- [Nonhomeomorphic closed aspherical four-manifolds](https://closedform.nishachay.tech/e/openai-math-2026-320/) - Entry 320 · A paper claims two closed aspherical 4-manifolds with the same homotopy type but no homeomorphism, against Borel. (Claimed, not checked)
- [A counterexample to Wall's finite D(2) problem](https://closedform.nishachay.tech/e/openai-math-2026-321/) - Entry 321 · A paper claims a negative answer to Wall's D(2) problem: a finite 3-complex that passes the test but has no 2-d model. (Claimed, not checked)
- [Metric Markov cotype of ℓ 1 and Hilbert-space Lipschitz extension](https://closedform.nishachay.tech/e/openai-math-2026-332/) - Entry 332 · Claims to prove that ℓ1 has metric Markov cotype two, settling Ball's extension problem for maps into ℓ1. (Claimed, not checked)
- [Gromov’s integral scalar-curvature bound for simplicial volume](https://closedform.nishachay.tech/e/openai-math-2026-335/) - Entry 335 · Claims Gromov's integral scalar-curvature bound for simplicial volume and the Gromov–Lawson aspherical conjecture. (Claimed, not checked)
- [Spectral scalar curvature, Urysohn width, and macroscopic dimension](https://closedform.nishachay.tech/e/openai-math-2026-336/) - Entry 336 · Claims Gromov's codimension-two width bound for positive scalar curvature in every dimension, and a spectral version. (Claimed, not checked)
- [Yau's uniformization conjecture](https://closedform.nishachay.tech/e/openai-math-2026-338/) - Entry 338 · Claims to prove Yau's uniformization conjecture: positive bisectional curvature makes a complete Kähler manifold ℂⁿ. (Claimed, not checked)
- [Katok's entropy rigidity conjecture](https://closedform.nishachay.tech/e/openai-math-2026-339/) - Entry 339 · Claims to prove Katok's entropy rigidity conjecture for negatively curved manifolds of dimension three and higher. (Claimed, not checked)
- [A counterexample to the nearby Lagrangian conjecture](https://closedform.nishachay.tech/e/openai-math-2026-340/) - Entry 340 · Claims a counterexample to Arnold's nearby Lagrangian conjecture, in the cotangent bundle of a product of two spheres. (Claimed, not checked)
- [Donaldson's hypersymplectic deformation conjecture](https://closedform.nishachay.tech/e/openai-math-2026-341/) - Entry 341 · Claims every hypersymplectic four-manifold deforms, with its cohomology classes fixed, to a hyperkähler triple. (Claimed, not checked)
- [The metric Blaschke conjecture](https://closedform.nishachay.tech/e/openai-math-2026-344/) - Entry 344 · Claims the metric Blaschke conjecture: injectivity radius equal to diameter forces a round sphere or projective space. (Claimed, not checked)
- [Infinitely many closed geodesics on Riemannian spheres and closed three-manifolds](https://closedform.nishachay.tech/e/openai-math-2026-345/) - Entry 345 · Claims every Riemannian metric on a sphere of any dimension has infinitely many geometrically distinct closed geodesics. (Claimed, not checked)
- [Sharp singular-set bounds for stationary integral varifolds](https://closedform.nishachay.tech/e/openai-math-2026-346/) - Entry 346 · Claims that the singular points of a stationary integral varifold have dimension at most one less than the varifold. (Claimed, not checked)
- [The Solomon–Yau least-volume conjecture](https://closedform.nishachay.tech/e/openai-math-2026-349/) - Entry 349 · Claims the Solomon–Yau conjecture: after the equator, the next minimal hypersurface of a sphere is a Clifford product. (Claimed, not checked)
- [Scalar curvature and finite-time Ricci-flow singularities](https://closedform.nishachay.tech/e/openai-math-2026-351/) - Entry 351 · Claims four-dimensional Ricci flow continues while scalar curvature is bounded, but not in some high dimension. (Claimed, not checked)
- [A finite-time singularity of Calabi flow](https://closedform.nishachay.tech/e/openai-math-2026-352/) - Entry 352 · Claims a smooth starting metric on complex projective 10-space whose Calabi flow breaks down in finite time. (Claimed, not checked)
- [Unique tangent flows at the first surface singularity](https://closedform.nishachay.tech/e/openai-math-2026-355/) - Entry 355 · Claims that blow-up limits of surface mean curvature flow are unique at the first singular time, in fixed coordinates. (Claimed, not checked)
- [Bi-Lipschitz coordinates at every regular RCD point](https://closedform.nishachay.tech/e/openai-math-2026-357/) - Entry 357 · Claims bi-Lipschitz coordinate charts around every regular point of a noncollapsed RCD space. (Claimed, not checked)
- [Kinetic limits and fluctuations over the Boltzmann lifespan](https://closedform.nishachay.tech/e/openai-math-2026-364/) - Entry 364 · Claims the Boltzmann equation follows from Newton's laws for short-range forces for as long as it stays regular. (Claimed, not checked)
- [The planar Mumford–Shah regularity conjecture and local weak- L 4 gradient bounds](https://closedform.nishachay.tech/e/openai-math-2026-366/) - Entry 366 · Claims interior Mumford–Shah regularity in the plane: edges are smooth arcs, crack tips or 120-degree triple junctions. (Claimed, not checked)
- [The three-dimensional Ball–Evans approximation problem](https://closedform.nishachay.tech/e/openai-math-2026-368/) - Entry 368 · Claims to solve the Ball–Evans problem in 3D: every Sobolev homeomorphism is a strong limit of smooth diffeomorphisms. (Claimed, not checked)
- [De Giorgi's conjecture in dimension eight](https://closedform.nishachay.tech/e/openai-math-2026-375/) - Entry 375 · Claims De Giorgi's conjecture in dimension eight: monotone Allen–Cahn solutions there are flat one-dimensional profiles. (Claimed, not checked)
- [Interior C^(1,α) regularity for infinity-harmonic functions](https://closedform.nishachay.tech/e/openai-math-2026-377/) - Entry 377 · Claims the gradient of every infinity-harmonic function is Hölder continuous inside its domain, in dimension 3 and up. (Claimed, not checked)

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