Closed Form — AI mathematics, explained https://closedform.nishachay.tech/ Newly explained entries from Closed Form, newest first. 377 · Claims the gradient of every infinity-harmonic function is Hölder continuous inside its domain, in dimension 3 and up. https://closedform.nishachay.tech/e/openai-math-2026-377/ https://closedform.nishachay.tech/e/openai-math-2026-377/ Wed, 14 Oct 2026 14:39:08 GMT 376 · Proves a pushed fluid can run any program: a marked particle enters a fixed box exactly when the program halts. https://closedform.nishachay.tech/e/openai-math-2026-376/ https://closedform.nishachay.tech/e/openai-math-2026-376/ Wed, 14 Oct 2026 14:39:08 GMT 375 · Claims De Giorgi's conjecture in dimension eight: monotone Allen–Cahn solutions there are flat one-dimensional profiles. https://closedform.nishachay.tech/e/openai-math-2026-375/ https://closedform.nishachay.tech/e/openai-math-2026-375/ Wed, 14 Oct 2026 14:39:08 GMT 374 · Proves optimal transport maps from a uniform convex source change at most like the cube root of the target change. https://closedform.nishachay.tech/e/openai-math-2026-374/ https://closedform.nishachay.tech/e/openai-math-2026-374/ Wed, 14 Oct 2026 14:39:08 GMT 373 · Proves that the best three-electron Coulomb arrangement need not follow fixed maps, even for a smooth density. https://closedform.nishachay.tech/e/openai-math-2026-373/ https://closedform.nishachay.tech/e/openai-math-2026-373/ Wed, 14 Oct 2026 14:39:08 GMT 372 · Proves that boundary push-and-measure data fix both stiffness values everywhere inside a smooth 3D elastic body. https://closedform.nishachay.tech/e/openai-math-2026-372/ https://closedform.nishachay.tech/e/openai-math-2026-372/ Wed, 14 Oct 2026 14:39:08 GMT 371 · Proves that blowup is stable for a defocusing Schrödinger equation on a 12-dimensional torus, for some large odd power. https://closedform.nishachay.tech/e/openai-math-2026-371/ https://closedform.nishachay.tech/e/openai-math-2026-371/ Wed, 14 Oct 2026 14:39:08 GMT 370 · Proves the subcritical Hénon–Lane–Emden conjecture: for small enough powers, these equations have no positive solution. https://closedform.nishachay.tech/e/openai-math-2026-370/ https://closedform.nishachay.tech/e/openai-math-2026-370/ Wed, 14 Oct 2026 14:39:08 GMT 369 · On smooth flat shapes without holes, the lasting hot and cold spots lie on the edge. https://closedform.nishachay.tech/e/openai-math-2026-369/ https://closedform.nishachay.tech/e/openai-math-2026-369/ Wed, 14 Oct 2026 14:39:08 GMT 368 · Claims to solve the Ball–Evans problem in 3D: every Sobolev homeomorphism is a strong limit of smooth diffeomorphisms. https://closedform.nishachay.tech/e/openai-math-2026-368/ https://closedform.nishachay.tech/e/openai-math-2026-368/ Wed, 14 Oct 2026 14:39:08 GMT 367 · Claims seven is the critical dimension for one-phase Bernoulli minimizers, so free boundaries are smooth through six. https://closedform.nishachay.tech/e/openai-math-2026-367/ https://closedform.nishachay.tech/e/openai-math-2026-367/ Wed, 14 Oct 2026 14:39:08 GMT 366 · Claims interior Mumford–Shah regularity in the plane: edges are smooth arcs, crack tips or 120-degree triple junctions. https://closedform.nishachay.tech/e/openai-math-2026-366/ https://closedform.nishachay.tech/e/openai-math-2026-366/ Wed, 14 Oct 2026 14:39:08 GMT 365 · Claims one boundary patch determines a smooth metric; proves rough 3D conductivities can share all boundary data. https://closedform.nishachay.tech/e/openai-math-2026-365/ https://closedform.nishachay.tech/e/openai-math-2026-365/ Wed, 14 Oct 2026 14:39:08 GMT 364 · Claims the Boltzmann equation follows from Newton's laws for short-range forces for as long as it stays regular. https://closedform.nishachay.tech/e/openai-math-2026-364/ https://closedform.nishachay.tech/e/openai-math-2026-364/ Wed, 14 Oct 2026 14:39:08 GMT 363 · Proves the periodic hard-sphere Boltzmann equation can have two different solutions from the same initial gas. https://closedform.nishachay.tech/e/openai-math-2026-363/ https://closedform.nishachay.tech/e/openai-math-2026-363/ Wed, 14 Oct 2026 14:39:08 GMT 362 · Proves the 3D relativistic Vlasov–Maxwell plasma equations have smooth solutions for all time, from any admissible data. https://closedform.nishachay.tech/e/openai-math-2026-362/ https://closedform.nishachay.tech/e/openai-math-2026-362/ Wed, 14 Oct 2026 14:39:08 GMT 361 · Proves Yau's Euclidean bound on polynomial-growth harmonic functions fails under nonnegative Ricci curvature. https://closedform.nishachay.tech/e/openai-math-2026-361/ https://closedform.nishachay.tech/e/openai-math-2026-361/ Wed, 14 Oct 2026 14:39:08 GMT 360 · Proves weak MTW curvature makes every injectivity domain convex, as Villani conjectured, and transport maps Hölder. https://closedform.nishachay.tech/e/openai-math-2026-360/ https://closedform.nishachay.tech/e/openai-math-2026-360/ Wed, 14 Oct 2026 14:39:08 GMT 359 · Proves a complete Kähler threefold with pinched negative curvature can lack bounded holomorphic coordinates. https://closedform.nishachay.tech/e/openai-math-2026-359/ https://closedform.nishachay.tech/e/openai-math-2026-359/ Wed, 14 Oct 2026 14:39:08 GMT 358 · Proves that a closed three-manifold can carry a metric without conjugate points yet no metric of nonpositive curvature. https://closedform.nishachay.tech/e/openai-math-2026-358/ https://closedform.nishachay.tech/e/openai-math-2026-358/ Wed, 14 Oct 2026 14:39:08 GMT 357 · Claims bi-Lipschitz coordinate charts around every regular point of a noncollapsed RCD space. https://closedform.nishachay.tech/e/openai-math-2026-357/ https://closedform.nishachay.tech/e/openai-math-2026-357/ Wed, 14 Oct 2026 14:39:08 GMT 356 · Claims Gigli's conjecture: Alexandrov curvature bounds match RCD spaces with a distributional sectional curvature bound. https://closedform.nishachay.tech/e/openai-math-2026-356/ https://closedform.nishachay.tech/e/openai-math-2026-356/ Wed, 14 Oct 2026 14:39:08 GMT 355 · Claims that blow-up limits of surface mean curvature flow are unique at the first singular time, in fixed coordinates. https://closedform.nishachay.tech/e/openai-math-2026-355/ https://closedform.nishachay.tech/e/openai-math-2026-355/ Wed, 14 Oct 2026 14:39:08 GMT 354 · Proves the isoperimetric conjecture for the cubic flat three-torus: balls, tubes, slabs and their complements. https://closedform.nishachay.tech/e/openai-math-2026-354/ https://closedform.nishachay.tech/e/openai-math-2026-354/ Wed, 14 Oct 2026 14:39:08 GMT 353 · Proves affine Bernstein rigidity for complete graphs in dimensions 3 to 9; claims a smooth dimension-ten counterexample. https://closedform.nishachay.tech/e/openai-math-2026-353/ https://closedform.nishachay.tech/e/openai-math-2026-353/ Wed, 14 Oct 2026 14:39:08 GMT 352 · Claims a smooth starting metric on complex projective 10-space whose Calabi flow breaks down in finite time. https://closedform.nishachay.tech/e/openai-math-2026-352/ https://closedform.nishachay.tech/e/openai-math-2026-352/ Wed, 14 Oct 2026 14:39:08 GMT 351 · Claims four-dimensional Ricci flow continues while scalar curvature is bounded, but not in some high dimension. https://closedform.nishachay.tech/e/openai-math-2026-351/ https://closedform.nishachay.tech/e/openai-math-2026-351/ Wed, 14 Oct 2026 14:39:08 GMT 350 · Proves Yau's sharp nodal-length bound on smooth surfaces, and shows it fails for smooth metrics in dimensions 3 to 5. https://closedform.nishachay.tech/e/openai-math-2026-350/ https://closedform.nishachay.tech/e/openai-math-2026-350/ Wed, 14 Oct 2026 14:39:08 GMT 349 · Claims the Solomon–Yau conjecture: after the equator, the next minimal hypersurface of a sphere is a Clifford product. https://closedform.nishachay.tech/e/openai-math-2026-349/ https://closedform.nishachay.tech/e/openai-math-2026-349/ Wed, 14 Oct 2026 14:39:08 GMT 348 · Classifies positive Einstein four-manifolds with nonnegative curvature, and claims a small-energy topological gap. https://closedform.nishachay.tech/e/openai-math-2026-348/ https://closedform.nishachay.tech/e/openai-math-2026-348/ Wed, 14 Oct 2026 14:39:08 GMT 347 · Claims counterexamples to strong forms of Arnold's fixed-point conjecture; the three-point quadric example is in Lean. https://closedform.nishachay.tech/e/openai-math-2026-347/ https://closedform.nishachay.tech/e/openai-math-2026-347/ Wed, 14 Oct 2026 14:39:08 GMT 346 · Claims that the singular points of a stationary integral varifold have dimension at most one less than the varifold. https://closedform.nishachay.tech/e/openai-math-2026-346/ https://closedform.nishachay.tech/e/openai-math-2026-346/ Wed, 14 Oct 2026 14:39:08 GMT 345 · Claims every Riemannian metric on a sphere of any dimension has infinitely many geometrically distinct closed geodesics. https://closedform.nishachay.tech/e/openai-math-2026-345/ https://closedform.nishachay.tech/e/openai-math-2026-345/ Wed, 14 Oct 2026 14:39:08 GMT 344 · Claims the metric Blaschke conjecture: injectivity radius equal to diameter forces a round sphere or projective space. https://closedform.nishachay.tech/e/openai-math-2026-344/ https://closedform.nishachay.tech/e/openai-math-2026-344/ Wed, 14 Oct 2026 14:39:08 GMT 343 · Proves Siegel and Yao's conjecture: from dimension six, ball packings are limited only by volume and the two-ball test. https://closedform.nishachay.tech/e/openai-math-2026-343/ https://closedform.nishachay.tech/e/openai-math-2026-343/ Wed, 14 Oct 2026 14:39:08 GMT 342 · Proves Donaldson's tamed-to-compatible conjecture for tamed almost-complex structures on closed four-manifolds. https://closedform.nishachay.tech/e/openai-math-2026-342/ https://closedform.nishachay.tech/e/openai-math-2026-342/ Wed, 14 Oct 2026 14:39:08 GMT 341 · Claims every hypersymplectic four-manifold deforms, with its cohomology classes fixed, to a hyperkähler triple. https://closedform.nishachay.tech/e/openai-math-2026-341/ https://closedform.nishachay.tech/e/openai-math-2026-341/ Wed, 14 Oct 2026 14:39:08 GMT 340 · Claims a counterexample to Arnold's nearby Lagrangian conjecture, in the cotangent bundle of a product of two spheres. https://closedform.nishachay.tech/e/openai-math-2026-340/ https://closedform.nishachay.tech/e/openai-math-2026-340/ Wed, 14 Oct 2026 14:39:08 GMT 339 · Claims to prove Katok's entropy rigidity conjecture for negatively curved manifolds of dimension three and higher. https://closedform.nishachay.tech/e/openai-math-2026-339/ https://closedform.nishachay.tech/e/openai-math-2026-339/ Wed, 14 Oct 2026 14:39:08 GMT 338 · Claims to prove Yau's uniformization conjecture: positive bisectional curvature makes a complete Kähler manifold ℂⁿ. https://closedform.nishachay.tech/e/openai-math-2026-338/ https://closedform.nishachay.tech/e/openai-math-2026-338/ Wed, 14 Oct 2026 14:39:08 GMT 337 · Proves sharp Euclidean fillings in CAT(0) spaces and claims the generalized Cartan–Hadamard isoperimetric inequality. https://closedform.nishachay.tech/e/openai-math-2026-337/ https://closedform.nishachay.tech/e/openai-math-2026-337/ Wed, 14 Oct 2026 14:39:08 GMT 336 · Claims Gromov's codimension-two width bound for positive scalar curvature in every dimension, and a spectral version. https://closedform.nishachay.tech/e/openai-math-2026-336/ https://closedform.nishachay.tech/e/openai-math-2026-336/ Wed, 14 Oct 2026 14:39:08 GMT 335 · Claims Gromov's integral scalar-curvature bound for simplicial volume and the Gromov–Lawson aspherical conjecture. https://closedform.nishachay.tech/e/openai-math-2026-335/ https://closedform.nishachay.tech/e/openai-math-2026-335/ Wed, 14 Oct 2026 14:39:08 GMT 334 · Some smooth rules for measuring length cannot be built as a surface in space, even near one point. https://closedform.nishachay.tech/e/openai-math-2026-334/ https://closedform.nishachay.tech/e/openai-math-2026-334/ Wed, 14 Oct 2026 14:39:08 GMT 333 · Proves that every closed smooth curved surface can be placed in four-dimensional space with all its distances kept. https://closedform.nishachay.tech/e/openai-math-2026-333/ https://closedform.nishachay.tech/e/openai-math-2026-333/ Wed, 14 Oct 2026 14:39:08 GMT 332 · Claims to prove that ℓ1 has metric Markov cotype two, settling Ball's extension problem for maps into ℓ1. https://closedform.nishachay.tech/e/openai-math-2026-332/ https://closedform.nishachay.tech/e/openai-math-2026-332/ Wed, 14 Oct 2026 14:39:08 GMT 331 · Proves a reflexive Banach space can be midpoint convex far out yet admit no asymptotically uniformly convex norm. https://closedform.nishachay.tech/e/openai-math-2026-331/ https://closedform.nishachay.tech/e/openai-math-2026-331/ Wed, 14 Oct 2026 14:39:08 GMT 330 · Proves a uniformly discrete metric space can have a Lipschitz-free space lacking the bounded approximation property. https://closedform.nishachay.tech/e/openai-math-2026-330/ https://closedform.nishachay.tech/e/openai-math-2026-330/ Wed, 14 Oct 2026 14:39:08 GMT 329 · Proves that the duality conjecture for metric entropy is false, already when the covering body is a cube. https://closedform.nishachay.tech/e/openai-math-2026-329/ https://closedform.nishachay.tech/e/openai-math-2026-329/ Wed, 14 Oct 2026 14:39:08 GMT 328 · Proves that every nonexpansive map of a closed bounded convex set in a reflexive Banach space has a fixed point. https://closedform.nishachay.tech/e/openai-math-2026-328/ https://closedform.nishachay.tech/e/openai-math-2026-328/ Wed, 14 Oct 2026 14:39:08 GMT 327 · Proves that a Banach space with nontrivial Markov type is superreflexive, answering a question of Naor. https://closedform.nishachay.tech/e/openai-math-2026-327/ https://closedform.nishachay.tech/e/openai-math-2026-327/ Wed, 14 Oct 2026 14:39:08 GMT 326 · For Banach spaces with the approximation property, K-convexity equals finite cotype of the space and its dual. https://closedform.nishachay.tech/e/openai-math-2026-326/ https://closedform.nishachay.tech/e/openai-math-2026-326/ Wed, 14 Oct 2026 14:39:08 GMT 325 · The complete Crouzeix conjecture holds: matrix-coefficient polynomials of an operator obey the sharp factor 2. https://closedform.nishachay.tech/e/openai-math-2026-325/ https://closedform.nishachay.tech/e/openai-math-2026-325/ Wed, 14 Oct 2026 14:39:08 GMT 324 · Two separable Banach spaces match distances up to fixed factors but are not linearly the same, answering Kalton. https://closedform.nishachay.tech/e/openai-math-2026-324/ https://closedform.nishachay.tech/e/openai-math-2026-324/ Wed, 14 Oct 2026 14:39:08 GMT 323 · The separable quotient problem cannot be settled from the usual axioms, a paper claims; Lean checks the CH half. https://closedform.nishachay.tech/e/openai-math-2026-323/ https://closedform.nishachay.tech/e/openai-math-2026-323/ Wed, 14 Oct 2026 14:39:08 GMT 322 · Every distance-keeping map between unit spheres of two real Banach spaces extends to a linear map of the spaces. https://closedform.nishachay.tech/e/openai-math-2026-322/ https://closedform.nishachay.tech/e/openai-math-2026-322/ Wed, 14 Oct 2026 14:39:08 GMT 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. https://closedform.nishachay.tech/e/openai-math-2026-321/ https://closedform.nishachay.tech/e/openai-math-2026-321/ Wed, 14 Oct 2026 14:39:08 GMT 320 · A paper claims two closed aspherical 4-manifolds with the same homotopy type but no homeomorphism, against Borel. https://closedform.nishachay.tech/e/openai-math-2026-320/ https://closedform.nishachay.tech/e/openai-math-2026-320/ Wed, 14 Oct 2026 14:39:08 GMT 319 · A paper claims to disprove the Hahn–Wilson conjecture at height two, for every large enough prime. https://closedform.nishachay.tech/e/openai-math-2026-319/ https://closedform.nishachay.tech/e/openai-math-2026-319/ Wed, 14 Oct 2026 14:39:08 GMT 318 · Five papers claim Hopkins' chromatic splitting conjecture fails in its strong and weak forms, and offer a filtered fix. https://closedform.nishachay.tech/e/openai-math-2026-318/ https://closedform.nishachay.tech/e/openai-math-2026-318/ Wed, 14 Oct 2026 14:39:08 GMT 317 · Strict n-categories carry a Thomason model structure in every dimension, settling an Ara–Maltsiniotis conjecture. https://closedform.nishachay.tech/e/openai-math-2026-317/ https://closedform.nishachay.tech/e/openai-math-2026-317/ Wed, 14 Oct 2026 14:39:08 GMT 316 · A paper claims to prove Curtis's 1975 conjecture: only η, ν, σ and Kervaire classes show up in mod-2 sphere homology. https://closedform.nishachay.tech/e/openai-math-2026-316/ https://closedform.nishachay.tech/e/openai-math-2026-316/ Wed, 14 Oct 2026 14:39:08 GMT 315 · Claims the Singer conjecture in dimension four: L²-Betti numbers of aspherical four-manifolds vanish off degree two. https://closedform.nishachay.tech/e/openai-math-2026-315/ https://closedform.nishachay.tech/e/openai-math-2026-315/ Wed, 14 Oct 2026 14:39:08 GMT 314 · Claims the exact chromatic loss between fixed points of p-group actions is a count of cyclic steps. https://closedform.nishachay.tech/e/openai-math-2026-314/ https://closedform.nishachay.tech/e/openai-math-2026-314/ Wed, 14 Oct 2026 14:39:08 GMT 313 · Claims every homotopy group of the K(n)-local sphere is finitely generated over the p-adic integers. https://closedform.nishachay.tech/e/openai-math-2026-313/ https://closedform.nishachay.tech/e/openai-math-2026-313/ Wed, 14 Oct 2026 14:39:08 GMT 312 · Grothendieck's algebraic ∞-groupoids capture all shapes of spaces, a paper claims, with its key step checked in Lean. https://closedform.nishachay.tech/e/openai-math-2026-312/ https://closedform.nishachay.tech/e/openai-math-2026-312/ Wed, 14 Oct 2026 14:39:08 GMT 311 · Claims Chai's invariant-ideal conjecture at every prime and height, and with it the Hovey–Strickland classification. https://closedform.nishachay.tech/e/openai-math-2026-311/ https://closedform.nishachay.tech/e/openai-math-2026-311/ Wed, 14 Oct 2026 14:39:08 GMT 310 · Claims Quillen's 1978 conjecture on subgroup posets for every finite group and every prime, in a stronger homology form. https://closedform.nishachay.tech/e/openai-math-2026-310/ https://closedform.nishachay.tech/e/openai-math-2026-310/ Wed, 14 Oct 2026 14:39:08 GMT 309 · Claims to settle which odd-primary Kervaire classes survive at the prime three: stems 10, 106 and 322. https://closedform.nishachay.tech/e/openai-math-2026-309/ https://closedform.nishachay.tech/e/openai-math-2026-309/ Wed, 14 Oct 2026 14:39:08 GMT 308 · Claims Smith–Toda complexes exist at every height if the prime may grow, with an explicit V(4) at the prime 1009. https://closedform.nishachay.tech/e/openai-math-2026-308/ https://closedform.nishachay.tech/e/openai-math-2026-308/ Wed, 14 Oct 2026 14:39:08 GMT 307 · Graph families where coarse assembly forgets a class of infinite order; Lean checks the reduced version. https://closedform.nishachay.tech/e/openai-math-2026-307/ https://closedform.nishachay.tech/e/openai-math-2026-307/ Wed, 14 Oct 2026 14:39:08 GMT 306 · Claims that two different surgeries on a nontrivial knot never give the same oriented three-dimensional space. https://closedform.nishachay.tech/e/openai-math-2026-306/ https://closedform.nishachay.tech/e/openai-math-2026-306/ Wed, 14 Oct 2026 14:39:08 GMT 305 · Claims the two-generator free group is not good for 4D surgery, plus a counterexample to Wall's question. https://closedform.nishachay.tech/e/openai-math-2026-305/ https://closedform.nishachay.tech/e/openai-math-2026-305/ Wed, 14 Oct 2026 14:39:08 GMT 304 · Claims a proof of Hilbert–Smith: a locally compact group acting faithfully on a connected manifold is a Lie group. https://closedform.nishachay.tech/e/openai-math-2026-304/ https://closedform.nishachay.tech/e/openai-math-2026-304/ Wed, 14 Oct 2026 14:39:08 GMT 303 · Proves pure infiniteness implies strong pure infiniteness in all C*-algebras, part of a Kirchberg–Rørdam question. https://closedform.nishachay.tech/e/openai-math-2026-303/ https://closedform.nishachay.tech/e/openai-math-2026-303/ Wed, 14 Oct 2026 14:39:08 GMT 302 · Claims the radius of comparison of a minimal crossed product is half the mean dimension, the Phillips–Toms conjecture. https://closedform.nishachay.tech/e/openai-math-2026-302/ https://closedform.nishachay.tech/e/openai-math-2026-302/ Wed, 14 Oct 2026 14:39:08 GMT 301 · Claims the trace cone determines every separable nuclear C*-algebra once stabilized by the Razak–Jacelon algebra. https://closedform.nishachay.tech/e/openai-math-2026-301/ https://closedform.nishachay.tech/e/openai-math-2026-301/ Wed, 14 Oct 2026 14:39:08 GMT 300 · Claims to settle both paving conjectures of Popa and Vaes for every maximal abelian subalgebra of a von Neumann algebra. https://closedform.nishachay.tech/e/openai-math-2026-300/ https://closedform.nishachay.tech/e/openai-math-2026-300/ Wed, 14 Oct 2026 14:39:08 GMT 299 · Proves a separable C*-algebra absorbs the Jiang–Su algebra exactly when its central-sequence algebra has no characters. https://closedform.nishachay.tech/e/openai-math-2026-299/ https://closedform.nishachay.tech/e/openai-math-2026-299/ Wed, 14 Oct 2026 14:39:08 GMT 298 · Proves two standard notions of free entropy can differ by at least 1/2 even when both are finite. https://closedform.nishachay.tech/e/openai-math-2026-298/ https://closedform.nishachay.tech/e/openai-math-2026-298/ Wed, 14 Oct 2026 14:39:08 GMT 297 · An algebra with one irreducible representation that is not the compact operators, built without extra axioms. https://closedform.nishachay.tech/e/openai-math-2026-297/ https://closedform.nishachay.tech/e/openai-math-2026-297/ Wed, 14 Oct 2026 14:39:08 GMT 296 · Every type II₁ factor with separable predual is generated by a single operator. https://closedform.nishachay.tech/e/openai-math-2026-296/ https://closedform.nishachay.tech/e/openai-math-2026-296/ Wed, 14 Oct 2026 14:39:08 GMT 295 · Proves bounded Hochschild cohomology of von Neumann algebras vanishes in degrees two and up, settling Kadison–Ringrose. https://closedform.nishachay.tech/e/openai-math-2026-295/ https://closedform.nishachay.tech/e/openai-math-2026-295/ Wed, 14 Oct 2026 14:39:08 GMT 294 · Proves Kaplansky's quasitrace conjecture false, and that stable finiteness can fail for tensor products. https://closedform.nishachay.tech/e/openai-math-2026-294/ https://closedform.nishachay.tech/e/openai-math-2026-294/ Wed, 14 Oct 2026 14:39:08 GMT 293 · Proves that some operators on Hilbert space have no hyperinvariant subspace, a negative answer to a long-open problem. https://closedform.nishachay.tech/e/openai-math-2026-293/ https://closedform.nishachay.tech/e/openai-math-2026-293/ Wed, 14 Oct 2026 14:39:08 GMT 292 · Proves, with a Lean check, an explicit C*-algebra that fits in no nuclear norm ultrapower, answering Kirchberg. https://closedform.nishachay.tech/e/openai-math-2026-292/ https://closedform.nishachay.tech/e/openai-math-2026-292/ Wed, 14 Oct 2026 14:39:08 GMT 291 · Claims amenable actions on Jiang–Su-stable algebras absorb the Jiang–Su algebra, plus three regularity theorems. https://closedform.nishachay.tech/e/openai-math-2026-291/ https://closedform.nishachay.tech/e/openai-math-2026-291/ Wed, 14 Oct 2026 14:39:08 GMT 290 · Claims every expected inclusion of von Neumann algebras holds an amenable piece with the same commutant in the core. https://closedform.nishachay.tech/e/openai-math-2026-290/ https://closedform.nishachay.tech/e/openai-math-2026-290/ Wed, 14 Oct 2026 14:39:08 GMT 289 · Proves, with a Lean check, that close von Neumann algebras are conjugate by a unitary near the identity, uniformly. https://closedform.nishachay.tech/e/openai-math-2026-289/ https://closedform.nishachay.tech/e/openai-math-2026-289/ Wed, 14 Oct 2026 14:39:08 GMT 288 · Every bounded map from a C*-algebra to operators can be straightened to respect the mirror operation. https://closedform.nishachay.tech/e/openai-math-2026-288/ https://closedform.nishachay.tech/e/openai-math-2026-288/ Wed, 14 Oct 2026 14:39:08 GMT 287 · Proves, with a Lean check, that the free group factors L(F₂) and L(F₃) are isomorphic, settling a decades-old problem. https://closedform.nishachay.tech/e/openai-math-2026-287/ https://closedform.nishachay.tech/e/openai-math-2026-287/ Wed, 14 Oct 2026 14:39:08 GMT 286 · Claims the von Neumann algebra of a property (T) lattice remembers its group, its twist and its scale. https://closedform.nishachay.tech/e/openai-math-2026-286/ https://closedform.nishachay.tech/e/openai-math-2026-286/ Wed, 14 Oct 2026 14:39:08 GMT 285 · Claims torsion-free groups that break the Kadison–Kaplansky projection conjecture and reduced Baum–Connes. https://closedform.nishachay.tech/e/openai-math-2026-285/ https://closedform.nishachay.tech/e/openai-math-2026-285/ Wed, 14 Oct 2026 14:39:08 GMT 284 · Claims functions where randomized queries need nearly the fourth power of quantum queries, refuting a cubic conjecture. https://closedform.nishachay.tech/e/openai-math-2026-284/ https://closedform.nishachay.tech/e/openai-math-2026-284/ Wed, 14 Oct 2026 14:39:08 GMT 283 · Claims a polynomial-size quantum circuit can carry out any n-qubit operation, given a suitable Boolean oracle. https://closedform.nishachay.tech/e/openai-math-2026-283/ https://closedform.nishachay.tech/e/openai-math-2026-283/ Wed, 14 Oct 2026 14:39:08 GMT 282 · Claims that scale symmetry forces local conformal symmetry for a broad class of four-dimensional quantum field theories. https://closedform.nishachay.tech/e/openai-math-2026-282/ https://closedform.nishachay.tech/e/openai-math-2026-282/ Wed, 14 Oct 2026 14:39:08 GMT 281 · Claims QAOA reaches the Sherrington–Kirkpatrick ground-state energy as size grows first and depth then increases. https://closedform.nishachay.tech/e/openai-math-2026-281/ https://closedform.nishachay.tech/e/openai-math-2026-281/ Wed, 14 Oct 2026 14:39:08 GMT 280 · Proves strongly rational unitary vertex operator algebras give conformal nets; claims their representations match. https://closedform.nishachay.tech/e/openai-math-2026-280/ https://closedform.nishachay.tech/e/openai-math-2026-280/ Wed, 14 Oct 2026 14:39:08 GMT 279 · Proves polynomial-size quantum circuits over a fixed gate set factor every integer with probability exactly one. https://closedform.nishachay.tech/e/openai-math-2026-279/ https://closedform.nishachay.tech/e/openai-math-2026-279/ Wed, 14 Oct 2026 14:39:08 GMT 278 · Claims a three-electron molecule whose ground-state density no Kohn–Sham ensemble can reproduce. https://closedform.nishachay.tech/e/openai-math-2026-278/ https://closedform.nishachay.tech/e/openai-math-2026-278/ Wed, 14 Oct 2026 14:39:08 GMT 277 · Proves that winning well above the entangled value in many repeated two-player games is exponentially unlikely. https://closedform.nishachay.tech/e/openai-math-2026-277/ https://closedform.nishachay.tech/e/openai-math-2026-277/ Wed, 14 Oct 2026 14:39:08 GMT 276 · Proves an exact formula for the classical capacity of every generalized amplitude-damping qubit channel. https://closedform.nishachay.tech/e/openai-math-2026-276/ https://closedform.nishachay.tech/e/openai-math-2026-276/ Wed, 14 Oct 2026 14:39:08 GMT 275 · Proves that estimating a molecule's exact electronic ground energy, from nuclear positions alone, is QMA-hard. https://closedform.nishachay.tech/e/openai-math-2026-275/ https://closedform.nishachay.tech/e/openai-math-2026-275/ Wed, 14 Oct 2026 14:39:08 GMT 274 · Proves constant-depth quantum circuits with polynomially many qubits cannot compute parity, settling Moore's conjecture. https://closedform.nishachay.tech/e/openai-math-2026-274/ https://closedform.nishachay.tech/e/openai-math-2026-274/ Wed, 14 Oct 2026 14:39:08 GMT 273 · Proves the entropy photon-number inequality for two independent finite-energy light inputs mixed on a beam splitter. https://closedform.nishachay.tech/e/openai-math-2026-273/ https://closedform.nishachay.tech/e/openai-math-2026-273/ Wed, 14 Oct 2026 14:39:08 GMT 272 · Claims an entangled state in local dimension ten that yields no secret key, answering a 2005 open problem. https://closedform.nishachay.tech/e/openai-math-2026-272/ https://closedform.nishachay.tech/e/openai-math-2026-272/ Wed, 14 Oct 2026 14:39:08 GMT 271 · Proves 3D quantum Heisenberg ferromagnets magnetize at low temperature; claims Bloch's T^(3/2) law and its correction. https://closedform.nishachay.tech/e/openai-math-2026-271/ https://closedform.nishachay.tech/e/openai-math-2026-271/ Wed, 14 Oct 2026 14:39:08 GMT 270 · Claims the BFSS matrix model has one zero-energy bound state for every N, and many positive-energy states at N = 2. https://closedform.nishachay.tech/e/openai-math-2026-270/ https://closedform.nishachay.tech/e/openai-math-2026-270/ Wed, 14 Oct 2026 14:39:08 GMT 269 · Proves a uniform energy gap of at least 1/25 above the Laughlin state on the sphere; claims it survives weak disorder. https://closedform.nishachay.tech/e/openai-math-2026-269/ https://closedform.nishachay.tech/e/openai-math-2026-269/ Wed, 14 Oct 2026 14:39:08 GMT 268 · Claims the spin-one Haldane gap: the Heisenberg chain on even rings has an energy gap that stays above log(20)/784. https://closedform.nishachay.tech/e/openai-math-2026-268/ https://closedform.nishachay.tech/e/openai-math-2026-268/ Wed, 14 Oct 2026 14:39:08 GMT 267 · Proves condensation in every ground state of the dilute hard-sphere Bose gas; claims thermal and depletion laws. https://closedform.nishachay.tech/e/openai-math-2026-267/ https://closedform.nishachay.tech/e/openai-math-2026-267/ Wed, 14 Oct 2026 14:39:08 GMT 266 · Dimension six fits only three mutually unbiased bases, by a computer-assisted search. https://closedform.nishachay.tech/e/openai-math-2026-266/ https://closedform.nishachay.tech/e/openai-math-2026-266/ Wed, 14 Oct 2026 14:39:08 GMT 265 · Claims the 2D area law: gapped ground states on a square grid hold entanglement proportional to boundary, not volume. https://closedform.nishachay.tech/e/openai-math-2026-265/ https://closedform.nishachay.tech/e/openai-math-2026-265/ Wed, 14 Oct 2026 14:39:08 GMT 264 · Claims typical vacuum perturbations of a rotating Kerr black hole cannot be smoothly continued past the inner horizon. https://closedform.nishachay.tech/e/openai-math-2026-264/ https://closedform.nishachay.tech/e/openai-math-2026-264/ Wed, 14 Oct 2026 14:39:08 GMT 263 · A nucleus can hold only a fixed number of extra electrons, however large its charge. https://closedform.nishachay.tech/e/openai-math-2026-263/ https://closedform.nishachay.tech/e/openai-math-2026-263/ Wed, 14 Oct 2026 14:39:08 GMT 262 · Proves the sharp 1D Lieb–Thirring constant for 1/2 < γ < 3/2; claims the matrix case and all equality cases. https://closedform.nishachay.tech/e/openai-math-2026-262/ https://closedform.nishachay.tech/e/openai-math-2026-262/ Wed, 14 Oct 2026 14:39:08 GMT 261 · Claims electrons stay trapped on a random square grid at any disorder, and can spread at weak disorder in 3D. https://closedform.nishachay.tech/e/openai-math-2026-261/ https://closedform.nishachay.tech/e/openai-math-2026-261/ Wed, 14 Oct 2026 14:39:08 GMT 260 · Claims the spacetime Penrose inequality: a black hole's enclosing area caps how small the total mass can be. https://closedform.nishachay.tech/e/openai-math-2026-260/ https://closedform.nishachay.tech/e/openai-math-2026-260/ Wed, 14 Oct 2026 14:39:08 GMT 259 · Claims a finitely generated group with two free measure-preserving actions of different costs, so fixed price fails. https://closedform.nishachay.tech/e/openai-math-2026-259/ https://closedform.nishachay.tech/e/openai-math-2026-259/ Wed, 14 Oct 2026 14:39:08 GMT 258 · Claims one-relator groups without Baumslag–Solitar subgroups are hyperbolic and virtually compact special. https://closedform.nishachay.tech/e/openai-math-2026-258/ https://closedform.nishachay.tech/e/openai-math-2026-258/ Wed, 14 Oct 2026 14:39:08 GMT 257 · A hyperbolic group that cannot act geometrically on any CAT(0) space, in any dimension. https://closedform.nishachay.tech/e/openai-math-2026-257/ https://closedform.nishachay.tech/e/openai-math-2026-257/ Wed, 14 Oct 2026 14:39:08 GMT 256 · Claims every nonsingular system of equations over any group is solvable in a larger group, settling Howie's conjecture. https://closedform.nishachay.tech/e/openai-math-2026-256/ https://closedform.nishachay.tech/e/openai-math-2026-256/ Wed, 14 Oct 2026 14:39:08 GMT 255 · Any finitely generated group that looks like a virtually polycyclic group from far away is virtually polycyclic. https://closedform.nishachay.tech/e/openai-math-2026-255/ https://closedform.nishachay.tech/e/openai-math-2026-255/ Wed, 14 Oct 2026 14:39:08 GMT 254 · Proves the Artin K(π,1) conjecture in finite rank, and finds an Artin group with no geometric CAT(0) action. https://closedform.nishachay.tech/e/openai-math-2026-254/ https://closedform.nishachay.tech/e/openai-math-2026-254/ Wed, 14 Oct 2026 14:39:08 GMT 253 · One infinite group that is simple, amenable and described by finitely many rules at once. https://closedform.nishachay.tech/e/openai-math-2026-253/ https://closedform.nishachay.tech/e/openai-math-2026-253/ Wed, 14 Oct 2026 14:39:08 GMT 252 · A torsion-free hyperbolic group in which some element vanishes in every finite quotient. https://closedform.nishachay.tech/e/openai-math-2026-252/ https://closedform.nishachay.tech/e/openai-math-2026-252/ Wed, 14 Oct 2026 14:39:08 GMT 251 · A discrete group is amenable exactly when every uniformly bounded representation can be made unitary. https://closedform.nishachay.tech/e/openai-math-2026-251/ https://closedform.nishachay.tech/e/openai-math-2026-251/ Wed, 14 Oct 2026 14:39:08 GMT 250 · A group has a word-solving algorithm exactly when it sits inside a finitely presented simple group. https://closedform.nishachay.tech/e/openai-math-2026-250/ https://closedform.nishachay.tech/e/openai-math-2026-250/ Wed, 14 Oct 2026 14:39:08 GMT 249 · Claims a group of cohomological dimension two with no two-dimensional classifying space, refuting Eilenberg–Ganea. https://closedform.nishachay.tech/e/openai-math-2026-249/ https://closedform.nishachay.tech/e/openai-math-2026-249/ Wed, 14 Oct 2026 14:39:08 GMT 248 · Thompson's group F, a famous group of interval stretchings, is not amenable. https://closedform.nishachay.tech/e/openai-math-2026-248/ https://closedform.nishachay.tech/e/openai-math-2026-248/ Wed, 14 Oct 2026 14:39:08 GMT 247 · Claims an infinite finitely presented group where every element has finite order, answering a Burnside question. https://closedform.nishachay.tech/e/openai-math-2026-247/ https://closedform.nishachay.tech/e/openai-math-2026-247/ Wed, 14 Oct 2026 14:39:08 GMT 246 · A hyperbolic group whose boundary is a sphere acts geometrically on hyperbolic three-space. https://closedform.nishachay.tech/e/openai-math-2026-246/ https://closedform.nishachay.tech/e/openai-math-2026-246/ Wed, 14 Oct 2026 14:39:08 GMT 245 · Claims that in every pure type system, if every legal term can finish computing, then every way of computing finishes. https://closedform.nishachay.tech/e/openai-math-2026-245/ https://closedform.nishachay.tech/e/openai-math-2026-245/ Wed, 14 Oct 2026 14:39:08 GMT 244 · Fitting sets back inside their images does not give you the Axiom of Choice. https://closedform.nishachay.tech/e/openai-math-2026-244/ https://closedform.nishachay.tech/e/openai-math-2026-244/ Wed, 14 Oct 2026 14:39:08 GMT 243 · Claims a polynomial-time query that choiceless polynomial time with counting cannot express. https://closedform.nishachay.tech/e/openai-math-2026-243/ https://closedform.nishachay.tech/e/openai-math-2026-243/ Wed, 14 Oct 2026 14:39:08 GMT 242 · Every computably listable set gets a whole-number polynomial test with exactly one solution per member. https://closedform.nishachay.tech/e/openai-math-2026-242/ https://closedform.nishachay.tech/e/openai-math-2026-242/ Wed, 14 Oct 2026 14:39:08 GMT 241 · Claims every symmetry of the Turing degrees is trivial, settling the rigidity question. https://closedform.nishachay.tech/e/openai-math-2026-241/ https://closedform.nishachay.tech/e/openai-math-2026-241/ Wed, 14 Oct 2026 14:39:08 GMT 240 · Claims Shelah's eventual categoricity conjecture in ZFC, and shows under CH that its proposed exact threshold fails. https://closedform.nishachay.tech/e/openai-math-2026-240/ https://closedform.nishachay.tech/e/openai-math-2026-240/ Wed, 14 Oct 2026 14:39:08 GMT 239 · Claims a random symmetric ±1 matrix is singular with probability (1/2 + o(1))ⁿ, with a matching biased-sign rate. https://closedform.nishachay.tech/e/openai-math-2026-239/ https://closedform.nishachay.tech/e/openai-math-2026-239/ Wed, 14 Oct 2026 14:39:08 GMT 238 · Claims the Thorp shuffle on 2^d cards randomizes the whole deck in order d shuffles, the best possible order. https://closedform.nishachay.tech/e/openai-math-2026-238/ https://closedform.nishachay.tech/e/openai-math-2026-238/ Wed, 14 Oct 2026 14:39:08 GMT 237 · Claims random self-avoiding walks of length n on the honeycomb lattice span about n^(3/4), the long-predicted exponent. https://closedform.nishachay.tech/e/openai-math-2026-237/ https://closedform.nishachay.tech/e/openai-math-2026-237/ Wed, 14 Oct 2026 14:39:08 GMT 236 · The free Ising state on a regular tree can be built from independent labels exactly up to tanh β = 1/√(d−1). https://closedform.nishachay.tech/e/openai-math-2026-236/ https://closedform.nishachay.tech/e/openai-math-2026-236/ Wed, 14 Oct 2026 14:39:08 GMT 235 · Random k-SAT has a single limiting satisfiability threshold for every k ≥ 3, and the 3-SAT one is computable. https://closedform.nishachay.tech/e/openai-math-2026-235/ https://closedform.nishachay.tech/e/openai-math-2026-235/ Wed, 14 Oct 2026 14:39:08 GMT 234 · A formula for the pressure of orthogonally invariant Ising spin glasses holds at every temperature. https://closedform.nishachay.tech/e/openai-math-2026-234/ https://closedform.nishachay.tech/e/openai-math-2026-234/ Wed, 14 Oct 2026 14:39:08 GMT 233 · Heights and current clusters of the critical Ashkin–Teller model converge together to a free field and its local sets. https://closedform.nishachay.tech/e/openai-math-2026-233/ https://closedform.nishachay.tech/e/openai-math-2026-233/ Wed, 14 Oct 2026 14:39:08 GMT 232 · Random Lipschitz height surfaces on the triangular lattice converge to the Gaussian free field. https://closedform.nishachay.tech/e/openai-math-2026-232/ https://closedform.nishachay.tech/e/openai-math-2026-232/ Wed, 14 Oct 2026 14:39:08 GMT 231 · One fixed rule builds the free uniform spanning forest from independent random labels on every infinite graph. https://closedform.nishachay.tech/e/openai-math-2026-231/ https://closedform.nishachay.tech/e/openai-math-2026-231/ Wed, 14 Oct 2026 14:39:08 GMT 230 · An explicit size rule gives every piece of an SLE random curve a positive, finite Hausdorff measure. https://closedform.nishachay.tech/e/openai-math-2026-230/ https://closedform.nishachay.tech/e/openai-math-2026-230/ Wed, 14 Oct 2026 14:39:08 GMT 229 · For three and four colors, guessing a tree's root from far leaves works exactly above the Kesten–Stigum bound. https://closedform.nishachay.tech/e/openai-math-2026-229/ https://closedform.nishachay.tech/e/openai-math-2026-229/ Wed, 14 Oct 2026 14:39:08 GMT 228 · Two built pair potentials give particles in space a first-order phase transition across a range of densities. https://closedform.nishachay.tech/e/openai-math-2026-228/ https://closedform.nishachay.tech/e/openai-math-2026-228/ Wed, 14 Oct 2026 14:39:08 GMT 227 · Heat-bath mixing in the SK spin glass is fast below β = 1, takes n^(2/3) at β = 1, and slows sharply above it. https://closedform.nishachay.tech/e/openai-math-2026-227/ https://closedform.nishachay.tech/e/openai-math-2026-227/ Wed, 14 Oct 2026 14:39:08 GMT 226 · Loops from two overlaid random domino tilings of the half-plane converge, as curves, to nested CLE₄. https://closedform.nishachay.tech/e/openai-math-2026-226/ https://closedform.nishachay.tech/e/openai-math-2026-226/ Wed, 14 Oct 2026 14:39:08 GMT 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). https://closedform.nishachay.tech/e/openai-math-2026-225/ https://closedform.nishachay.tech/e/openai-math-2026-225/ Wed, 14 Oct 2026 14:39:08 GMT 224 · Cardy's formula holds for Poisson–Voronoi percolation, and near-critical thresholds match the triangular lattice. https://closedform.nishachay.tech/e/openai-math-2026-224/ https://closedform.nishachay.tech/e/openai-math-2026-224/ Wed, 14 Oct 2026 14:39:08 GMT 223 · Critical random-cluster interfaces on the square grid converge to SLE curves for every cluster weight up to 4. https://closedform.nishachay.tech/e/openai-math-2026-223/ https://closedform.nishachay.tech/e/openai-math-2026-223/ Wed, 14 Oct 2026 14:39:08 GMT 222 · Exact free energies for Ising and spherical perceptrons at every density, and the gap and force exponents at jamming. https://closedform.nishachay.tech/e/openai-math-2026-222/ https://closedform.nishachay.tech/e/openai-math-2026-222/ Wed, 14 Oct 2026 14:39:08 GMT 221 · The Mézard–Parisi cavity formula gives the exact free energy of sparse spin glasses in the Panchenko–Talagrand class. https://closedform.nishachay.tech/e/openai-math-2026-221/ https://closedform.nishachay.tech/e/openai-math-2026-221/ Wed, 14 Oct 2026 14:39:08 GMT 220 · A walk in a random environment escapes in a given direction with probability 0 or 1, and escape forces positive speed. https://closedform.nishachay.tech/e/openai-math-2026-220/ https://closedform.nishachay.tech/e/openai-math-2026-220/ Wed, 14 Oct 2026 14:39:08 GMT 219 · Eigenvalue spacings of random regular graphs, even with weak random potentials, match those of Gaussian random matrices. https://closedform.nishachay.tech/e/openai-math-2026-219/ https://closedform.nishachay.tech/e/openai-math-2026-219/ Wed, 14 Oct 2026 14:39:08 GMT 218 · Weak extra interactions or weak random bonds leave the critical Ising interface's conformal limit, SLE₃, unchanged. https://closedform.nishachay.tech/e/openai-math-2026-218/ https://closedform.nishachay.tech/e/openai-math-2026-218/ Wed, 14 Oct 2026 14:39:08 GMT 217 · The typical spread of the low-temperature Sherrington–Kirkpatrick free energy grows like n^(1/6), with a limiting law. https://closedform.nishachay.tech/e/openai-math-2026-217/ https://closedform.nishachay.tech/e/openai-math-2026-217/ Wed, 14 Oct 2026 14:39:08 GMT 216 · Six papers claim exact critical laws for the planar XY model, as the Berezinskii–Kosterlitz–Thouless picture predicts. https://closedform.nishachay.tech/e/openai-math-2026-216/ https://closedform.nishachay.tech/e/openai-math-2026-216/ Wed, 14 Oct 2026 14:39:08 GMT 215 · Spin models with three or more components are proved to lose alignment exponentially at every temperature. https://closedform.nishachay.tech/e/openai-math-2026-215/ https://closedform.nishachay.tech/e/openai-math-2026-215/ Wed, 14 Oct 2026 14:39:08 GMT 214 · Percolation on every fast-spreading symmetric graph has a range with infinitely many endless clusters. https://closedform.nishachay.tech/e/openai-math-2026-214/ https://closedform.nishachay.tech/e/openai-math-2026-214/ Wed, 14 Oct 2026 14:39:08 GMT 213 · At the exact tipping point, random networks of a broad, symmetric kind form no endless cluster. https://closedform.nishachay.tech/e/openai-math-2026-213/ https://closedform.nishachay.tech/e/openai-math-2026-213/ Wed, 14 Oct 2026 14:39:08 GMT 212 · Planar random-metric grids are claimed to have no route that is fastest forever both ways, and a smooth limit shape. https://closedform.nishachay.tech/e/openai-math-2026-212/ https://closedform.nishachay.tech/e/openai-math-2026-212/ Wed, 14 Oct 2026 14:39:08 GMT 211 · Random FK planar maps are claimed to look like random surfaces for q ≤ 4 and like a random tree above 4. https://closedform.nishachay.tech/e/openai-math-2026-211/ https://closedform.nishachay.tech/e/openai-math-2026-211/ Wed, 14 Oct 2026 14:39:08 GMT 210 · Foulkes' conjecture is claimed for sixth powers, with a Lean-proved bound past which a natural map is onto. https://closedform.nishachay.tech/e/openai-math-2026-210/ https://closedform.nishachay.tech/e/openai-math-2026-210/ Wed, 14 Oct 2026 14:39:08 GMT 209 · Two ramified rings are claimed to break Gersten's conjecture: nonzero K-theory classes vanish over their fractions. https://closedform.nishachay.tech/e/openai-math-2026-209/ https://closedform.nishachay.tech/e/openai-math-2026-209/ Wed, 14 Oct 2026 14:39:08 GMT 208 · Every finite symmetric tensor category in characteristic p is claimed to map into one higher Verlinde category. https://closedform.nishachay.tech/e/openai-math-2026-208/ https://closedform.nishachay.tech/e/openai-math-2026-208/ Wed, 14 Oct 2026 14:39:08 GMT 207 · Idempotents in group rings carry no trace at infinite-order elements, for every group; Kaplansky's problem follows. https://closedform.nishachay.tech/e/openai-math-2026-207/ https://closedform.nishachay.tech/e/openai-math-2026-207/ Wed, 14 Oct 2026 14:39:08 GMT 206 · Some finite lattices are not the congruence lattice of any finite algebra, and no program can tell which. https://closedform.nishachay.tech/e/openai-math-2026-206/ https://closedform.nishachay.tech/e/openai-math-2026-206/ Wed, 14 Oct 2026 14:39:08 GMT 205 · The staircase representation's tensor square contains every irreducible representation, proving Saxl's conjecture. https://closedform.nishachay.tech/e/openai-math-2026-205/ https://closedform.nishachay.tech/e/openai-math-2026-205/ Wed, 14 Oct 2026 14:39:08 GMT 204 · For even spin groups, an invariant after stretching the weights implies one before, if the weights pass a parity test. https://closedform.nishachay.tech/e/openai-math-2026-204/ https://closedform.nishachay.tech/e/openai-math-2026-204/ Wed, 14 Oct 2026 14:39:08 GMT 203 · Two papers claim Donovan's conjecture: blocks with bounded defect fall into finitely many types, for every prime. https://closedform.nishachay.tech/e/openai-math-2026-203/ https://closedform.nishachay.tech/e/openai-math-2026-203/ Wed, 14 Oct 2026 14:39:08 GMT 202 · A paper claims to prove Alperin's weight conjecture, block by block, for every finite group and every prime. https://closedform.nishachay.tech/e/openai-math-2026-202/ https://closedform.nishachay.tech/e/openai-math-2026-202/ Wed, 14 Oct 2026 14:39:08 GMT 201 · A division ring made from two elements, each element algebraic, can still be infinite-dimensional over its center. https://closedform.nishachay.tech/e/openai-math-2026-201/ https://closedform.nishachay.tech/e/openai-math-2026-201/ Wed, 14 Oct 2026 14:39:08 GMT 200 · Two papers claim the Eisenbud–Green–Harris and lex-plus-powers conjectures over every field of characteristic zero. https://closedform.nishachay.tech/e/openai-math-2026-200/ https://closedform.nishachay.tech/e/openai-math-2026-200/ Wed, 14 Oct 2026 14:39:08 GMT 199 · A module with no self-extensions in any degree can still fail to be projective, against Auslander–Reiten and Tachikawa. https://closedform.nishachay.tech/e/openai-math-2026-199/ https://closedform.nishachay.tech/e/openai-math-2026-199/ Wed, 14 Oct 2026 14:39:08 GMT 198 · An algebra with finite resolutions of every length refutes the little finitistic-dimension conjecture. https://closedform.nishachay.tech/e/openai-math-2026-198/ https://closedform.nishachay.tech/e/openai-math-2026-198/ Wed, 14 Oct 2026 14:39:08 GMT 197 · In some group algebras, a left inverse is not a right inverse, which disproves Kaplansky's direct-finiteness conjecture. https://closedform.nishachay.tech/e/openai-math-2026-197/ https://closedform.nishachay.tech/e/openai-math-2026-197/ Wed, 14 Oct 2026 14:39:08 GMT 196 · A group with no looping moves still lets two nonzero sums multiply to zero. https://closedform.nishachay.tech/e/openai-math-2026-196/ https://closedform.nishachay.tech/e/openai-math-2026-196/ Wed, 14 Oct 2026 14:39:08 GMT 195 · A three-dimensional complete local domain over the complex numbers has no small Cohen–Macaulay module. https://closedform.nishachay.tech/e/openai-math-2026-195/ https://closedform.nishachay.tech/e/openai-math-2026-195/ Wed, 14 Oct 2026 14:39:08 GMT 194 · Hilbert–Samuel multiplicity is claimed never to drop along a flat local map, settling Lech's 1960 conjecture. https://closedform.nishachay.tech/e/openai-math-2026-194/ https://closedform.nishachay.tech/e/openai-math-2026-194/ Wed, 14 Oct 2026 14:39:08 GMT 193 · Serre's intersection multiplicity is claimed to be strictly positive over every regular local ring. https://closedform.nishachay.tech/e/openai-math-2026-193/ https://closedform.nishachay.tech/e/openai-math-2026-193/ Wed, 14 Oct 2026 14:39:08 GMT 192 · Boolean functions can beat the proposed square-root-of-degree bound on their linear correlations by any factor. https://closedform.nishachay.tech/e/openai-math-2026-192/ https://closedform.nishachay.tech/e/openai-math-2026-192/ Wed, 14 Oct 2026 14:39:08 GMT 191 · Some n points in a unit square keep every triangle above n^(−2+η) in area, beating 1/n² by a fixed power. https://closedform.nishachay.tech/e/openai-math-2026-191/ https://closedform.nishachay.tech/e/openai-math-2026-191/ Wed, 14 Oct 2026 14:39:08 GMT 190 · One fixed 66×66 pattern of zeros and ones has no polynomial removal bound in ordered binary matrices. https://closedform.nishachay.tech/e/openai-math-2026-190/ https://closedform.nishachay.tech/e/openai-math-2026-190/ Wed, 14 Oct 2026 14:39:08 GMT 189 · Exact Ramsey numbers for a cycle versus a clique: R(C_m, K_n) = (m − 1)(n − 1) + 1 when m ≥ n ≥ 3. https://closedform.nishachay.tech/e/openai-math-2026-189/ https://closedform.nishachay.tech/e/openai-math-2026-189/ Wed, 14 Oct 2026 14:39:08 GMT 188 · Randomly erasing triangles from a complete graph leaves about n^(3/2)/(2√2) edges at the end. https://closedform.nishachay.tech/e/openai-math-2026-188/ https://closedform.nishachay.tech/e/openai-math-2026-188/ Wed, 14 Oct 2026 14:39:08 GMT 187 · On an endless grid, the first player can always build the six-square Snaky shape within 21 moves. https://closedform.nishachay.tech/e/openai-math-2026-187/ https://closedform.nishachay.tech/e/openai-math-2026-187/ Wed, 14 Oct 2026 14:39:08 GMT 186 · Every symmetric increasing graph property switches on within a window of width about 1/(log n)². https://closedform.nishachay.tech/e/openai-math-2026-186/ https://closedform.nishachay.tech/e/openai-math-2026-186/ Wed, 14 Oct 2026 14:39:08 GMT 185 · Two self-dual infinite matroids break the infinite matroid packing/covering and intersection conjectures. https://closedform.nishachay.tech/e/openai-math-2026-185/ https://closedform.nishachay.tech/e/openai-math-2026-185/ Wed, 14 Oct 2026 14:39:08 GMT 184 · Networks with no fixed-size clique have larger independent sets and need fewer colors, by a log factor. https://closedform.nishachay.tech/e/openai-math-2026-184/ https://closedform.nishachay.tech/e/openai-math-2026-184/ Wed, 14 Oct 2026 14:39:08 GMT 183 · The maximum number of halving lines for n points in the plane is below n to the power 4/3 by a fixed margin. https://closedform.nishachay.tech/e/openai-math-2026-183/ https://closedform.nishachay.tech/e/openai-math-2026-183/ Wed, 14 Oct 2026 14:39:08 GMT 182 · Sets of whole numbers with no square difference are smaller than N by a fixed power of N. https://closedform.nishachay.tech/e/openai-math-2026-182/ https://closedform.nishachay.tech/e/openai-math-2026-182/ Wed, 14 Oct 2026 14:39:08 GMT 181 · Every network on n points splits into at most a fixed multiple of n loops and single links. https://closedform.nishachay.tech/e/openai-math-2026-181/ https://closedform.nishachay.tech/e/openai-math-2026-181/ Wed, 14 Oct 2026 14:39:08 GMT 180 · Every Barnette graph has a round trip through all its points. https://closedform.nishachay.tech/e/openai-math-2026-180/ https://closedform.nishachay.tech/e/openai-math-2026-180/ Wed, 14 Oct 2026 14:39:08 GMT 179 · Circulant Hadamard matrices exist only in sizes 1 and 4. https://closedform.nishachay.tech/e/openai-math-2026-179/ https://closedform.nishachay.tech/e/openai-math-2026-179/ Wed, 14 Oct 2026 14:39:08 GMT 178 · A fixed recipe builds networks with best-possible mixing, in every degree and every large even size. https://closedform.nishachay.tech/e/openai-math-2026-178/ https://closedform.nishachay.tech/e/openai-math-2026-178/ Wed, 14 Oct 2026 14:39:08 GMT 177 · Large higher-dimensional expanders with a bounded number of faces at each point exist in every dimension. https://closedform.nishachay.tech/e/openai-math-2026-177/ https://closedform.nishachay.tech/e/openai-math-2026-177/ Wed, 14 Oct 2026 14:39:08 GMT 176 · A random graph contains a target graph soon after simple expected counts say it could, up to a log factor. https://closedform.nishachay.tech/e/openai-math-2026-176/ https://closedform.nishachay.tech/e/openai-math-2026-176/ Wed, 14 Oct 2026 14:39:08 GMT 175 · Spreading credit fractionally beats whole-set covers by at most a fixed factor in Talagrand's threshold theory. https://closedform.nishachay.tech/e/openai-math-2026-175/ https://closedform.nishachay.tech/e/openai-math-2026-175/ Wed, 14 Oct 2026 14:39:08 GMT 174 · Every k-connected network has a spanning tree that uses at most a fixed multiple of 1/k of every cut. https://closedform.nishachay.tech/e/openai-math-2026-174/ https://closedform.nishachay.tech/e/openai-math-2026-174/ Wed, 14 Oct 2026 14:39:08 GMT 173 · In every network of one-way arrows, some point reaches at least as many points in two steps as in one. https://closedform.nishachay.tech/e/openai-math-2026-173/ https://closedform.nishachay.tech/e/openai-math-2026-173/ Wed, 14 Oct 2026 14:39:08 GMT 172 · An exact algebraic test tells which finite point sets must appear in one color in any coloring of space. https://closedform.nishachay.tech/e/openai-math-2026-172/ https://closedform.nishachay.tech/e/openai-math-2026-172/ Wed, 14 Oct 2026 14:39:08 GMT 171 · Two-coloring the links among a constant times 2ⁿ points always gives a one-color n-dimensional cube, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-171/ https://closedform.nishachay.tech/e/openai-math-2026-171/ Wed, 14 Oct 2026 14:39:08 GMT 170 · For every fixed s ≥ 5, the Ramsey number r(s,t) now has its exact power of log t, up to a vanishing error. https://closedform.nishachay.tech/e/openai-math-2026-170/ https://closedform.nishachay.tech/e/openai-math-2026-170/ Wed, 14 Oct 2026 14:39:08 GMT 169 · A coloring count with an extra q-weight always splits into elementary pieces with nonnegative coefficients. https://closedform.nishachay.tech/e/openai-math-2026-169/ https://closedform.nishachay.tech/e/openai-math-2026-169/ Wed, 14 Oct 2026 14:39:08 GMT 168 · Proves a Kazhdan–Lusztig polynomial depends only on the shape of its Bruhat interval, settling combinatorial invariance. https://closedform.nishachay.tech/e/openai-math-2026-168/ https://closedform.nishachay.tech/e/openai-math-2026-168/ Wed, 14 Oct 2026 14:39:08 GMT 167 · Proves almost every point in a large planar set sees nearly n distances, and lowers the unit-distance exponent 4/3. https://closedform.nishachay.tech/e/openai-math-2026-167/ https://closedform.nishachay.tech/e/openai-math-2026-167/ Wed, 14 Oct 2026 14:39:08 GMT 166 · Any n points in d ≥ 3 dimensions span at least a constant times n^(2/d) distinct distances, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-166/ https://closedform.nishachay.tech/e/openai-math-2026-166/ Wed, 14 Oct 2026 14:39:08 GMT 165 · The classic crossing formulas for drawing complete networks are exact. https://closedform.nishachay.tech/e/openai-math-2026-165/ https://closedform.nishachay.tech/e/openai-math-2026-165/ Wed, 14 Oct 2026 14:39:08 GMT 164 · However whole numbers are colored, some set of each size has its sums and products in one color, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-164/ https://closedform.nishachay.tech/e/openai-math-2026-164/ Wed, 14 Oct 2026 14:39:08 GMT 162 · Ryser's covering conjecture is false: some intersecting hypergraphs with r parts need r vertices to cover. https://closedform.nishachay.tech/e/openai-math-2026-162/ https://closedform.nishachay.tech/e/openai-math-2026-162/ Wed, 14 Oct 2026 14:39:08 GMT 161 · A 35-vertex bipartite pattern appears less often in some graph than random would predict. https://closedform.nishachay.tech/e/openai-math-2026-161/ https://closedform.nishachay.tech/e/openai-math-2026-161/ Wed, 14 Oct 2026 14:39:08 GMT 160 · Proves van der Waerden numbers grow faster than any exponential, answering a question of Erdős for two colors. https://closedform.nishachay.tech/e/openai-math-2026-160/ https://closedform.nishachay.tech/e/openai-math-2026-160/ Wed, 14 Oct 2026 14:39:08 GMT 159 · Any set of whole numbers whose reciprocals add to infinity holds evenly spaced runs of every length. https://closedform.nishachay.tech/e/openai-math-2026-159/ https://closedform.nishachay.tech/e/openai-math-2026-159/ Wed, 14 Oct 2026 14:39:08 GMT 158 · No way of coloring the plane with five colors keeps every unit-distance pair apart. https://closedform.nishachay.tech/e/openai-math-2026-158/ https://closedform.nishachay.tech/e/openai-math-2026-158/ Wed, 14 Oct 2026 14:39:08 GMT 157 · Proves Hadwiger's 1943 coloring conjecture is false, and that a fixed multiple of the minor size still bounds coloring. https://closedform.nishachay.tech/e/openai-math-2026-157/ https://closedform.nishachay.tech/e/openai-math-2026-157/ Wed, 14 Oct 2026 14:39:08 GMT 156 · A set in nine-dimensional space cannot be cut into ten smaller pieces, so Borsuk's conjecture fails there. https://closedform.nishachay.tech/e/openai-math-2026-156/ https://closedform.nishachay.tech/e/openai-math-2026-156/ Wed, 14 Oct 2026 14:39:08 GMT 155 · Proves a finite tile in three dimensions can tile space, yet never in a fully repeating pattern. https://closedform.nishachay.tech/e/openai-math-2026-155/ https://closedform.nishachay.tech/e/openai-math-2026-155/ Wed, 14 Oct 2026 14:39:08 GMT 154 · For mixing systems, averages along k, 2k, …, nk are claimed to settle at almost every starting point, for every n. https://closedform.nishachay.tech/e/openai-math-2026-154/ https://closedform.nishachay.tech/e/openai-math-2026-154/ Wed, 14 Oct 2026 14:39:08 GMT 153 · Claimed singular Bernoulli convolutions beyond Pisot reciprocals, plus an arithmetic test for every parameter. https://closedform.nishachay.tech/e/openai-math-2026-153/ https://closedform.nishachay.tech/e/openai-math-2026-153/ Wed, 14 Oct 2026 14:39:08 GMT 152 · An abstract zero-entropy system with no smooth, volume-keeping copy in any dimension. https://closedform.nishachay.tech/e/openai-math-2026-152/ https://closedform.nishachay.tech/e/openai-math-2026-152/ Wed, 14 Oct 2026 14:39:08 GMT 151 · A smooth-enough map can double a shape's homology while its orbits stay orderly. https://closedform.nishachay.tech/e/openai-math-2026-151/ https://closedform.nishachay.tech/e/openai-math-2026-151/ Wed, 14 Oct 2026 14:39:08 GMT 150 · A paper claims billiards in every triangle with an irrational angle forget their start: they are weakly mixing. https://closedform.nishachay.tech/e/openai-math-2026-150/ https://closedform.nishachay.tech/e/openai-math-2026-150/ Wed, 14 Oct 2026 14:39:08 GMT 149 · With fixed rates, every weakly reversible chemical network herds each class of states into one common window. https://closedform.nishachay.tech/e/openai-math-2026-149/ https://closedform.nishachay.tech/e/openai-math-2026-149/ Wed, 14 Oct 2026 14:39:08 GMT 148 · A single formula gives the dimension of every self-similar measure on the line, even when its pieces collide. https://closedform.nishachay.tech/e/openai-math-2026-148/ https://closedform.nishachay.tech/e/openai-math-2026-148/ Wed, 14 Oct 2026 14:39:08 GMT 147 · Two papers claim that a smooth billiard table with an unbroken band of caustics along its edge must be an ellipse. https://closedform.nishachay.tech/e/openai-math-2026-147/ https://closedform.nishachay.tech/e/openai-math-2026-147/ Wed, 14 Oct 2026 14:39:08 GMT 146 · The standard map is chaotic on a region of positive area for every large enough parameter. https://closedform.nishachay.tech/e/openai-math-2026-146/ https://closedform.nishachay.tech/e/openai-math-2026-146/ Wed, 14 Oct 2026 14:39:08 GMT 145 · If long waits make any two moments independent, they make every finite group of moments independent. https://closedform.nishachay.tech/e/openai-math-2026-145/ https://closedform.nishachay.tech/e/openai-math-2026-145/ Wed, 14 Oct 2026 14:39:08 GMT 144 · A smooth map of a 3D torus where one measurement’s past and future build every average-zero measurement. https://closedform.nishachay.tech/e/openai-math-2026-144/ https://closedform.nishachay.tech/e/openai-math-2026-144/ Wed, 14 Oct 2026 14:39:08 GMT 143 · Claims a finite cap, set by degree alone, on limit cycles of planar polynomial systems. https://closedform.nishachay.tech/e/openai-math-2026-143/ https://closedform.nishachay.tech/e/openai-math-2026-143/ Wed, 14 Oct 2026 14:39:08 GMT 142 · A claimed coin-free algorithm that factors any polynomial modulo a prime in time polynomial in the input size. https://closedform.nishachay.tech/e/openai-math-2026-142/ https://closedform.nishachay.tech/e/openai-math-2026-142/ Wed, 14 Oct 2026 14:39:08 GMT 141 · Deciding “there is x so that for every y” questions about real numbers claimed at one fixed counting level. https://closedform.nishachay.tech/e/openai-math-2026-141/ https://closedform.nishachay.tech/e/openai-math-2026-141/ Wed, 14 Oct 2026 14:39:08 GMT 140 · Exact clues still cost more reading for each extra digit of accuracy when memory is limited. https://closedform.nishachay.tech/e/openai-math-2026-140/ https://closedform.nishachay.tech/e/openai-math-2026-140/ Wed, 14 Oct 2026 14:39:08 GMT 139 · Sampling from a gently curved bowl needs no fixed power of the dimension in queries. https://closedform.nishachay.tech/e/openai-math-2026-139/ https://closedform.nishachay.tech/e/openai-math-2026-139/ Wed, 14 Oct 2026 14:39:08 GMT 138 · A randomized algorithm claims to decide every Subset Sum instance in O(2^(0.49n)) time, below the 2^(n/2) scale. https://closedform.nishachay.tech/e/openai-math-2026-138/ https://closedform.nishachay.tech/e/openai-math-2026-138/ Wed, 14 Oct 2026 14:39:08 GMT 137 · A one-tape machine's run can be replayed with far less memory than the old square-root rule allowed. https://closedform.nishachay.tech/e/openai-math-2026-137/ https://closedform.nishachay.tech/e/openai-math-2026-137/ Wed, 14 Oct 2026 14:39:08 GMT 136 · End-of-Line puzzles turn into number circuits only slightly bigger that tolerate many broken gates, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-136/ https://closedform.nishachay.tech/e/openai-math-2026-136/ Wed, 14 Oct 2026 14:39:08 GMT 135 · Five-layer recipes for multiplying n matrices need n to a power that grows like √n. https://closedform.nishachay.tech/e/openai-math-2026-135/ https://closedform.nishachay.tech/e/openai-math-2026-135/ Wed, 14 Oct 2026 14:39:08 GMT 134 · Three nested stars are enough to describe any regular language once complement is allowed. https://closedform.nishachay.tech/e/openai-math-2026-134/ https://closedform.nishachay.tech/e/openai-math-2026-134/ Wed, 14 Oct 2026 14:39:08 GMT 133 · Deciding Weisfeiler–Leman equivalence at dimension k needs time n to a power proportional to k. https://closedform.nishachay.tech/e/openai-math-2026-133/ https://closedform.nishachay.tech/e/openai-math-2026-133/ Wed, 14 Oct 2026 14:39:08 GMT 132 · Block sensitivity can outgrow any constant times sensitivity squared. https://closedform.nishachay.tech/e/openai-math-2026-132/ https://closedform.nishachay.tech/e/openai-math-2026-132/ Wed, 14 Oct 2026 14:39:08 GMT 131 · Random rewiring reaches a fair random network quickly, for every possible list of degrees. https://closedform.nishachay.tech/e/openai-math-2026-131/ https://closedform.nishachay.tech/e/openai-math-2026-131/ Wed, 14 Oct 2026 14:39:08 GMT 130 · In exact arithmetic, the discrete Fourier transform can be computed in slightly fewer than n log n steps. https://closedform.nishachay.tech/e/openai-math-2026-130/ https://closedform.nishachay.tech/e/openai-math-2026-130/ Wed, 14 Oct 2026 14:39:08 GMT 129 · Removing guesses from simple two-way reading machines can cost exponentially many states. https://closedform.nishachay.tech/e/openai-math-2026-129/ https://closedform.nishachay.tech/e/openai-math-2026-129/ Wed, 14 Oct 2026 14:39:08 GMT 128 · A fast method builds a string containing all given pieces, never more than twice the shortest possible. https://closedform.nishachay.tech/e/openai-math-2026-128/ https://closedform.nishachay.tech/e/openai-math-2026-128/ Wed, 14 Oct 2026 14:39:08 GMT 127 · Yes-or-no rules built from degree-d polynomials on n inputs have average sensitivity at most 8d√n. https://closedform.nishachay.tech/e/openai-math-2026-127/ https://closedform.nishachay.tech/e/openai-math-2026-127/ Wed, 14 Oct 2026 14:39:08 GMT 126 · Exact semidefinite descriptions of perfect matching need exponential size, a new paper claims. https://closedform.nishachay.tech/e/openai-math-2026-126/ https://closedform.nishachay.tech/e/openai-math-2026-126/ Wed, 14 Oct 2026 14:39:08 GMT 125 · The best possible guarantee for placing k facilities is exactly 1 + 2/e, assuming P ≠ NP. https://closedform.nishachay.tech/e/openai-math-2026-125/ https://closedform.nishachay.tech/e/openai-math-2026-125/ Wed, 14 Oct 2026 14:39:08 GMT 124 · The best schedule for one-hour jobs with order rules on three machines can be found in polynomial time. https://closedform.nishachay.tech/e/openai-math-2026-124/ https://closedform.nishachay.tech/e/openai-math-2026-124/ Wed, 14 Oct 2026 14:39:08 GMT 122 · Rebuilding a string from randomly thinned copies needs more than polynomially many copies. https://closedform.nishachay.tech/e/openai-math-2026-122/ https://closedform.nishachay.tech/e/openai-math-2026-122/ Wed, 14 Oct 2026 14:39:08 GMT 121 · Edit distance can be estimated to within any fixed accuracy in barely more than linear time. https://closedform.nishachay.tech/e/openai-math-2026-121/ https://closedform.nishachay.tech/e/openai-math-2026-121/ Wed, 14 Oct 2026 14:39:08 GMT 120 · A randomized algorithm finds a largest matching in any graph in almost-linear time, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-120/ https://closedform.nishachay.tech/e/openai-math-2026-120/ Wed, 14 Oct 2026 14:39:08 GMT 119 · No yes-or-no summary of random bits survives noise better than simply keeping one bit. https://closedform.nishachay.tech/e/openai-math-2026-119/ https://closedform.nishachay.tech/e/openai-math-2026-119/ Wed, 14 Oct 2026 14:39:08 GMT 118 · Rounding up the fractional bin count can be wrong by any fixed number of bins. https://closedform.nishachay.tech/e/openai-math-2026-118/ https://closedform.nishachay.tech/e/openai-math-2026-118/ Wed, 14 Oct 2026 14:39:08 GMT 117 · Finding a network's weakest split even roughly is claimed NP-hard, and a key relaxation can miss by almost √log n. https://closedform.nishachay.tech/e/openai-math-2026-117/ https://closedform.nishachay.tech/e/openai-math-2026-117/ Wed, 14 Oct 2026 14:39:08 GMT 116 · One fixed set of matrices exposes every nonzero small formula whose variables do not commute. https://closedform.nishachay.tech/e/openai-math-2026-116/ https://closedform.nishachay.tech/e/openai-math-2026-116/ Wed, 14 Oct 2026 14:39:08 GMT 115 · Number grids with fixed row and column sums can be sampled fairly and counted fast, whatever their size. https://closedform.nishachay.tech/e/openai-math-2026-115/ https://closedform.nishachay.tech/e/openai-math-2026-115/ Wed, 14 Oct 2026 14:39:08 GMT 114 · Shared solutions of two capacity rules can be counted approximately, at a cost set by digits, not size. https://closedform.nishachay.tech/e/openai-math-2026-114/ https://closedform.nishachay.tech/e/openai-math-2026-114/ Wed, 14 Oct 2026 14:39:08 GMT 113 · A fast coin-flipping method estimates the number of perfect matchings in any network, to any chosen accuracy. https://closedform.nishachay.tech/e/openai-math-2026-113/ https://closedform.nishachay.tech/e/openai-math-2026-113/ Wed, 14 Oct 2026 14:39:08 GMT 112 · One fast-to-decide problem needs three-layer circuits bigger than any 2^(A√n) for large inputs. https://closedform.nishachay.tech/e/openai-math-2026-112/ https://closedform.nishachay.tech/e/openai-math-2026-112/ Wed, 14 Oct 2026 14:39:08 GMT 111 · One sample per item lets an online rule keep a fixed share of the best, even against an all-seeing opponent. https://closedform.nishachay.tech/e/openai-math-2026-111/ https://closedform.nishachay.tech/e/openai-math-2026-111/ Wed, 14 Oct 2026 14:39:08 GMT 110 · Randomized k-server costs at most a squared-logarithm factor on every space, matching the known lower bound. https://closedform.nishachay.tech/e/openai-math-2026-110/ https://closedform.nishachay.tech/e/openai-math-2026-110/ Wed, 14 Oct 2026 14:39:08 GMT 109 · A tape-based computer can multiply huge whole numbers slightly faster than the long-conjectured n log n limit. https://closedform.nishachay.tech/e/openai-math-2026-109/ https://closedform.nishachay.tech/e/openai-math-2026-109/ Wed, 14 Oct 2026 14:39:08 GMT 108 · Disguising the permanent as a determinant needs a matrix that grows at least like the cube of its size. https://closedform.nishachay.tech/e/openai-math-2026-108/ https://closedform.nishachay.tech/e/openai-math-2026-108/ Wed, 14 Oct 2026 14:39:08 GMT 107 · Huge n-by-n complex matrices can be multiplied in about n^(9/4) arithmetic steps, up to any tiny slack. https://closedform.nishachay.tech/e/openai-math-2026-107/ https://closedform.nishachay.tech/e/openai-math-2026-107/ Wed, 14 Oct 2026 14:39:08 GMT 106 · Even a three-colorable graph can be NP-hard to tell from one with only tiny independent sets. https://closedform.nishachay.tech/e/openai-math-2026-106/ https://closedform.nishachay.tech/e/openai-math-2026-106/ Wed, 14 Oct 2026 14:39:08 GMT 105 · Telling fully solvable 2-to-1 games from nearly worthless ones is NP-hard. https://closedform.nishachay.tech/e/openai-math-2026-105/ https://closedform.nishachay.tech/e/openai-math-2026-105/ Wed, 14 Oct 2026 14:39:08 GMT 104 · Who wins a mean-payoff game can be found in quasipolynomial time, however large the scores. https://closedform.nishachay.tech/e/openai-math-2026-104/ https://closedform.nishachay.tech/e/openai-math-2026-104/ Wed, 14 Oct 2026 14:39:08 GMT 103 · Coin flips give no extra power to computers with tiny memory: L = RL = BPL. https://closedform.nishachay.tech/e/openai-math-2026-103/ https://closedform.nishachay.tech/e/openai-math-2026-103/ Wed, 14 Oct 2026 14:39:08 GMT 102 · Telling almost-solvable puzzles from hopeless ones can be impossibly hard. https://closedform.nishachay.tech/e/openai-math-2026-102/ https://closedform.nishachay.tech/e/openai-math-2026-102/ Wed, 14 Oct 2026 14:39:08 GMT 101 · In every dimension, simplices alone have the largest isotropic constant among convex bodies, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-101/ https://closedform.nishachay.tech/e/openai-math-2026-101/ Wed, 14 Oct 2026 14:39:08 GMT 100 · Cylinders can cover a regular tetrahedron for less than half its smallest shadow. https://closedform.nishachay.tech/e/openai-math-2026-100/ https://closedform.nishachay.tech/e/openai-math-2026-100/ Wed, 14 Oct 2026 14:39:08 GMT 099 · Edit distance between words can be drawn as ℓ1 distance only with distortion of size exp(√(log d·log log d)). https://closedform.nishachay.tech/e/openai-math-2026-099/ https://closedform.nishachay.tech/e/openai-math-2026-099/ Wed, 14 Oct 2026 14:39:08 GMT 098 · Some uncrowded point sets in infinite dimensions cannot be copied faithfully into any finite dimension. https://closedform.nishachay.tech/e/openai-math-2026-098/ https://closedform.nishachay.tech/e/openai-math-2026-098/ Wed, 14 Oct 2026 14:39:08 GMT 097 · One choice of signs keeps every running total of unit vectors within a constant times √d, at any length. https://closedform.nishachay.tech/e/openai-math-2026-097/ https://closedform.nishachay.tech/e/openai-math-2026-097/ Wed, 14 Oct 2026 14:39:08 GMT 096 · Three 120-degree wedges are the best way to cut a bell-curve cloud, in every dimension. https://closedform.nishachay.tech/e/openai-math-2026-096/ https://closedform.nishachay.tech/e/openai-math-2026-096/ Wed, 14 Oct 2026 14:39:08 GMT 095 · A claimed proof that some hyperbolicity cones have no semidefinite description, even with hidden variables. https://closedform.nishachay.tech/e/openai-math-2026-095/ https://closedform.nishachay.tech/e/openai-math-2026-095/ Wed, 14 Oct 2026 14:39:08 GMT 094 · Points in Lp space can be squeezed into far fewer coordinates if distances may stretch slightly. https://closedform.nishachay.tech/e/openai-math-2026-094/ https://closedform.nishachay.tech/e/openai-math-2026-094/ Wed, 14 Oct 2026 14:39:08 GMT 093 · Log-concave laws with bell-curve tails in every direction obey a dimension-free log-Sobolev bound, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-093/ https://closedform.nishachay.tech/e/openai-math-2026-093/ Wed, 14 Oct 2026 14:39:08 GMT 092 · The worst convex shape needs covering density about n log n in dimension n, lattice or not. https://closedform.nishachay.tech/e/openai-math-2026-092/ https://closedform.nishachay.tech/e/openai-math-2026-092/ Wed, 14 Oct 2026 14:39:08 GMT 091 · Blending two symmetric shapes the thrifty way never loses volume below their geometric mean. https://closedform.nishachay.tech/e/openai-math-2026-091/ https://closedform.nishachay.tech/e/openai-math-2026-091/ Wed, 14 Oct 2026 14:39:08 GMT 090 · No arrangement of points in the plane beats the triangular lattice for any steadily fading repulsion. https://closedform.nishachay.tech/e/openai-math-2026-090/ https://closedform.nishachay.tech/e/openai-math-2026-090/ Wed, 14 Oct 2026 14:39:08 GMT 089 · Every planar road network can be redrawn in taxicab distance with stretch below one fixed number. https://closedform.nishachay.tech/e/openai-math-2026-089/ https://closedform.nishachay.tech/e/openai-math-2026-089/ Wed, 14 Oct 2026 14:39:08 GMT 088 · In four or more dimensions, ellipsoids have the smallest shadow body for their volume. https://closedform.nishachay.tech/e/openai-math-2026-088/ https://closedform.nishachay.tech/e/openai-math-2026-088/ Wed, 14 Oct 2026 14:39:08 GMT 087 · Symmetric convex bodies cannot beat Mahler's volume bound. https://closedform.nishachay.tech/e/openai-math-2026-087/ https://closedform.nishachay.tech/e/openai-math-2026-087/ Wed, 14 Oct 2026 14:39:08 GMT 086 · A singular average of three shifted functions obeys an L³ × L³ × L³ to L¹ size bound, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-086/ https://closedform.nishachay.tech/e/openai-math-2026-086/ Wed, 14 Oct 2026 14:39:08 GMT 085 · Taking the best disk average at each point never multiplies a surface's total slope by more than a fixed factor. https://closedform.nishachay.tech/e/openai-math-2026-085/ https://closedform.nishachay.tech/e/openai-math-2026-085/ Wed, 14 Oct 2026 14:39:08 GMT 084 · A set covering almost all of [0, 1] can dodge every copy of a geometric list like 1/2, 1/4, 1/8, … https://closedform.nishachay.tech/e/openai-math-2026-084/ https://closedform.nishachay.tech/e/openai-math-2026-084/ Wed, 14 Oct 2026 14:39:08 GMT 083 · Hilbert transforms along any Lipschitz direction field in the plane obey one energy bound at short lengths. https://closedform.nishachay.tech/e/openai-math-2026-083/ https://closedform.nishachay.tech/e/openai-math-2026-083/ Wed, 14 Oct 2026 14:39:08 GMT 082 · A triangle-shaped singular integral stays bounded at the symmetric L³ point, whatever cutoffs each point picks. https://closedform.nishachay.tech/e/openai-math-2026-082/ https://closedform.nishachay.tech/e/openai-math-2026-082/ Wed, 14 Oct 2026 14:39:08 GMT 081 · A bounded Riesz transform forces surfaces in higher codimension to contain big flat-like pieces. https://closedform.nishachay.tech/e/openai-math-2026-081/ https://closedform.nishachay.tech/e/openai-math-2026-081/ Wed, 14 Oct 2026 14:39:08 GMT 080 · Claimed proofs that Schrödinger waves return to rough data at the exact smoothness threshold, in dimensions n ≥ 2. https://closedform.nishachay.tech/e/openai-math-2026-080/ https://closedform.nishachay.tech/e/openai-math-2026-080/ Wed, 14 Oct 2026 14:39:08 GMT 079 · A claimed proof of Sogge's local smoothing conjecture for waves in 3D space, including the critical case p = 3. https://closedform.nishachay.tech/e/openai-math-2026-079/ https://closedform.nishachay.tech/e/openai-math-2026-079/ Wed, 14 Oct 2026 14:39:08 GMT 078 · A claimed proof of the Bochner–Riesz conjecture in three dimensions, in its strict-order form. https://closedform.nishachay.tech/e/openai-math-2026-078/ https://closedform.nishachay.tech/e/openai-math-2026-078/ Wed, 14 Oct 2026 14:39:08 GMT 077 · Claimed proofs of the full Fourier restriction range p > 3 for the sphere and for positively curved surfaces. https://closedform.nishachay.tech/e/openai-math-2026-077/ https://closedform.nishachay.tech/e/openai-math-2026-077/ Wed, 14 Oct 2026 14:39:08 GMT 076 · Polynomials with only +1 and −1 coefficients can be almost perfectly flat on the unit circle. https://closedform.nishachay.tech/e/openai-math-2026-076/ https://closedform.nishachay.tech/e/openai-math-2026-076/ Wed, 14 Oct 2026 14:39:08 GMT 075 · Fourier sums of every L log L function converge to it at almost every point of the circle. https://closedform.nishachay.tech/e/openai-math-2026-075/ https://closedform.nishachay.tech/e/openai-math-2026-075/ Wed, 14 Oct 2026 14:39:08 GMT 074 · Claimed proofs: the Kakeya maximal conjecture in 3D, and full dimension for every Kakeya set in 4D. https://closedform.nishachay.tech/e/openai-math-2026-074/ https://closedform.nishachay.tech/e/openai-math-2026-074/ Wed, 14 Oct 2026 14:39:08 GMT 073 · Any closed, bounded set whose dimension is more than half that of its space has distances with positive total length. https://closedform.nishachay.tech/e/openai-math-2026-073/ https://closedform.nishachay.tech/e/openai-math-2026-073/ Wed, 14 Oct 2026 14:39:08 GMT 072 · Reshaping a region into a disk can never squeeze too hard: Brennan's 1978 conjecture is proved. https://closedform.nishachay.tech/e/openai-math-2026-072/ https://closedform.nishachay.tech/e/openai-math-2026-072/ Wed, 14 Oct 2026 14:39:08 GMT 071 · Every region of the sphere, however many holes it has, can be reshaped so that each hole is round. https://closedform.nishachay.tech/e/openai-math-2026-071/ https://closedform.nishachay.tech/e/openai-math-2026-071/ Wed, 14 Oct 2026 14:39:08 GMT 069 · A claimed proof of quantum geometric Langlands duality on any smooth complex curve at every irrational level. https://closedform.nishachay.tech/e/openai-math-2026-069/ https://closedform.nishachay.tech/e/openai-math-2026-069/ Wed, 14 Oct 2026 14:39:08 GMT 068 · A claimed proof that a smooth nonnegatively curved anticanonical bundle always has a section of some power. https://closedform.nishachay.tech/e/openai-math-2026-068/ https://closedform.nishachay.tech/e/openai-math-2026-068/ Wed, 14 Oct 2026 14:39:08 GMT 067 · A claimed proof that every six-dimensional Fano manifold with nef tangent bundle is a symmetric, homogeneous space. https://closedform.nishachay.tech/e/openai-math-2026-067/ https://closedform.nishachay.tech/e/openai-math-2026-067/ Wed, 14 Oct 2026 14:39:08 GMT 066 · One complement index, fixed by dimension and singularity bound, works for every mildly singular Fano contraction. https://closedform.nishachay.tech/e/openai-math-2026-066/ https://closedform.nishachay.tech/e/openai-math-2026-066/ Wed, 14 Oct 2026 14:39:08 GMT 065 · Claimed proofs that curve counts on complete intersections and on projective bundles obey the Virasoro equations. https://closedform.nishachay.tech/e/openai-math-2026-065/ https://closedform.nishachay.tech/e/openai-math-2026-065/ Wed, 14 Oct 2026 14:39:08 GMT 064 · A claimed proof that surface singularities with a constant Milnor number keep the same topology along a family. https://closedform.nishachay.tech/e/openai-math-2026-064/ https://closedform.nishachay.tech/e/openai-math-2026-064/ Wed, 14 Oct 2026 14:39:08 GMT 063 · A claimed proof that rational curves on a Fano manifold cap its Picard number, with equality only for product spaces. https://closedform.nishachay.tech/e/openai-math-2026-063/ https://closedform.nishachay.tech/e/openai-math-2026-063/ Wed, 14 Oct 2026 14:39:08 GMT 062 · Contact Fano manifolds are homogeneous, which settles the LeBrun–Salamon conjecture on quaternionic-Kähler spaces. https://closedform.nishachay.tech/e/openai-math-2026-062/ https://closedform.nishachay.tech/e/openai-math-2026-062/ Wed, 14 Oct 2026 14:39:08 GMT 060 · Every minimal class VII surface with positive second Betti number contains a global spherical shell. https://closedform.nishachay.tech/e/openai-math-2026-060/ https://closedform.nishachay.tech/e/openai-math-2026-060/ Wed, 14 Oct 2026 14:39:08 GMT 059 · Two hypersurface germs with the same embedded topology but different multiplicities, against Zariski’s 1971 question. https://closedform.nishachay.tech/e/openai-math-2026-059/ https://closedform.nishachay.tech/e/openai-math-2026-059/ Wed, 14 Oct 2026 14:39:08 GMT 058 · Unrolled shapes with a polynomial description split into just three kinds of pieces. https://closedform.nishachay.tech/e/openai-math-2026-058/ https://closedform.nishachay.tech/e/openai-math-2026-058/ Wed, 14 Oct 2026 14:39:08 GMT 057 · Special compact Kähler manifolds claim virtually abelian fundamental groups in every dimension, as Campana predicted. https://closedform.nishachay.tech/e/openai-math-2026-057/ https://closedform.nishachay.tech/e/openai-math-2026-057/ Wed, 14 Oct 2026 14:39:08 GMT 056 · Every permitted minimal model program on a projective log canonical fourfold claims to stop after finitely many steps. https://closedform.nishachay.tech/e/openai-math-2026-056/ https://closedform.nishachay.tech/e/openai-math-2026-056/ Wed, 14 Oct 2026 14:39:08 GMT 055 · A stability condition on every smooth quintic threefold with Toda’s exact 2/5 Gepner symmetry. https://closedform.nishachay.tech/e/openai-math-2026-055/ https://closedform.nishachay.tech/e/openai-math-2026-055/ Wed, 14 Oct 2026 14:39:08 GMT 054 · Very general cubic fourfolds of large admissible discriminant are irrational despite a K3 derived category. https://closedform.nishachay.tech/e/openai-math-2026-054/ https://closedform.nishachay.tech/e/openai-math-2026-054/ Wed, 14 Oct 2026 14:39:08 GMT 053 · A tautological relation in genus 10^60 that Pixton’s original relations miss, in Chow and in cohomology. https://closedform.nishachay.tech/e/openai-math-2026-053/ https://closedform.nishachay.tech/e/openai-math-2026-053/ Wed, 14 Oct 2026 14:39:08 GMT 052 · Two integrable families of directions on a compact Kähler manifold make its universal cover a product. https://closedform.nishachay.tech/e/openai-math-2026-052/ https://closedform.nishachay.tech/e/openai-math-2026-052/ Wed, 14 Oct 2026 14:39:08 GMT 051 · Compact Kähler manifolds with no entire curves have ample canonical bundle, as Kobayashi conjectured. https://closedform.nishachay.tech/e/openai-math-2026-051/ https://closedform.nishachay.tech/e/openai-math-2026-051/ Wed, 14 Oct 2026 14:39:08 GMT 050 · Algebraic positivity need not come with positive curvature, even on the simple surface built from two spheres. https://closedform.nishachay.tech/e/openai-math-2026-050/ https://closedform.nishachay.tech/e/openai-math-2026-050/ Wed, 14 Oct 2026 14:39:08 GMT 049 · A polynomial that becomes a coordinate with one extra variable, but not without it, disproves two conjectures. https://closedform.nishachay.tech/e/openai-math-2026-049/ https://closedform.nishachay.tech/e/openai-math-2026-049/ Wed, 14 Oct 2026 14:39:08 GMT 048 · A singular complex surface whose vector fields still form a free basis, against the Lipman–Zariski conjecture. https://closedform.nishachay.tech/e/openai-math-2026-048/ https://closedform.nishachay.tech/e/openai-math-2026-048/ Wed, 14 Oct 2026 14:39:08 GMT 047 · A four-dimensional shape that is not ordinary space, until you add one line. https://closedform.nishachay.tech/e/openai-math-2026-047/ https://closedform.nishachay.tech/e/openai-math-2026-047/ Wed, 14 Oct 2026 14:39:08 GMT 046 · Two claimed counterexamples to Shafarevich's conjecture: a surface and a fourfold whose universal covers fail convexity. https://closedform.nishachay.tech/e/openai-math-2026-046/ https://closedform.nishachay.tech/e/openai-math-2026-046/ Wed, 14 Oct 2026 14:39:08 GMT 044 · For every finite quiver, the cohomology of a Nakajima variety is claimed to equal functions on a Coulomb fixed scheme. https://closedform.nishachay.tech/e/openai-math-2026-044/ https://closedform.nishachay.tech/e/openai-math-2026-044/ Wed, 14 Oct 2026 14:39:08 GMT 043 · Two ways of layering the cohomology of SL_n Higgs moduli are claimed to agree in every composite coprime rank. https://closedform.nishachay.tech/e/openai-math-2026-043/ https://closedform.nishachay.tech/e/openai-math-2026-043/ Wed, 14 Oct 2026 14:39:08 GMT 042 · A claimed proof that every complex K3 surface is Oka: local holomorphic maps into it can be copied by entire maps. https://closedform.nishachay.tech/e/openai-math-2026-042/ https://closedform.nishachay.tech/e/openai-math-2026-042/ Wed, 14 Oct 2026 14:39:08 GMT 041 · Every nonzero nef isotropic line bundle on a compact hyperkähler manifold is claimed to give a torus fibration. https://closedform.nishachay.tech/e/openai-math-2026-041/ https://closedform.nishachay.tech/e/openai-math-2026-041/ Wed, 14 Oct 2026 14:39:08 GMT 040 · On a complex surface with no holomorphic two-forms, zero-cycles carry only their degree and Albanese data. https://closedform.nishachay.tech/e/openai-math-2026-040/ https://closedform.nishachay.tech/e/openai-math-2026-040/ Wed, 14 Oct 2026 14:39:08 GMT 039 · Nagata's 1959 rule for curves through random points holds for every count from 10 points up. https://closedform.nishachay.tech/e/openai-math-2026-039/ https://closedform.nishachay.tech/e/openai-math-2026-039/ Wed, 14 Oct 2026 14:39:08 GMT 038 · On every smooth shape, n + 1 copies of a positive bundle are always enough for Fujita's freeness. https://closedform.nishachay.tech/e/openai-math-2026-038/ https://closedform.nishachay.tech/e/openai-math-2026-038/ Wed, 14 Oct 2026 14:39:08 GMT 037 · Every singular point of a mild kind is at most as roomy as a double cone, in any dimension. https://closedform.nishachay.tech/e/openai-math-2026-037/ https://closedform.nishachay.tech/e/openai-math-2026-037/ Wed, 14 Oct 2026 14:39:08 GMT 036 · Nef adjoint divisors with an extra nef part are claimed to be numerically semiample; minimal models are claimed too. https://closedform.nishachay.tech/e/openai-math-2026-036/ https://closedform.nishachay.tech/e/openai-math-2026-036/ Wed, 14 Oct 2026 14:39:08 GMT 035 · In characteristic above 3, a nef log canonical threefold divisor of numerical dimension one is claimed to give a map. https://closedform.nishachay.tech/e/openai-math-2026-035/ https://closedform.nishachay.tech/e/openai-math-2026-035/ Wed, 14 Oct 2026 14:39:08 GMT 034 · A family of 14 papers claims log abundance in characteristic zero and the effective Iitaka fibration conjecture. https://closedform.nishachay.tech/e/openai-math-2026-034/ https://closedform.nishachay.tech/e/openai-math-2026-034/ Wed, 14 Oct 2026 14:39:08 GMT 033 · Twisting a family of shapes never destroys the forms its fibers and base contribute. https://closedform.nishachay.tech/e/openai-math-2026-033/ https://closedform.nishachay.tech/e/openai-math-2026-033/ Wed, 14 Oct 2026 14:39:08 GMT 032 · The rational Hodge conjecture is claimed for every abelian variety with complex multiplication, in every dimension. https://closedform.nishachay.tech/e/openai-math-2026-032/ https://closedform.nishachay.tech/e/openai-math-2026-032/ Wed, 14 Oct 2026 14:39:08 GMT 031 · Every open map between these Galois groups is claimed to come from a unique map between the fields. https://closedform.nishachay.tech/e/openai-math-2026-031/ https://closedform.nishachay.tech/e/openai-math-2026-031/ Wed, 14 Oct 2026 14:39:08 GMT 030 · Every elliptic curve over every imaginary quadratic field is claimed to match an automorphic form, place by place. https://closedform.nishachay.tech/e/openai-math-2026-030/ https://closedform.nishachay.tech/e/openai-math-2026-030/ Wed, 14 Oct 2026 14:39:08 GMT 029 · Every whole number except −1 and perfect squares is claimed to be a primitive root for infinitely many primes. https://closedform.nishachay.tech/e/openai-math-2026-029/ https://closedform.nishachay.tech/e/openai-math-2026-029/ Wed, 14 Oct 2026 14:39:08 GMT 028 · No walk through Gaussian primes with steps of bounded length can go on forever. https://closedform.nishachay.tech/e/openai-math-2026-028/ https://closedform.nishachay.tech/e/openai-math-2026-028/ Wed, 14 Oct 2026 14:39:08 GMT 027 · On every curve, whole-number matrix rules spread across the character variety after one enlargement of the integers. https://closedform.nishachay.tech/e/openai-math-2026-027/ https://closedform.nishachay.tech/e/openai-math-2026-027/ Wed, 14 Oct 2026 14:39:08 GMT 026 · For any size bar, a fixed share of prime gaps clears it, all the way out. https://closedform.nishachay.tech/e/openai-math-2026-026/ https://closedform.nishachay.tech/e/openai-math-2026-026/ Wed, 14 Oct 2026 14:39:08 GMT 025 · Every fraction below 1 is a sum of about log log b distinct unit fractions, as Erdős conjectured. https://closedform.nishachay.tech/e/openai-math-2026-025/ https://closedform.nishachay.tech/e/openai-math-2026-025/ Wed, 14 Oct 2026 14:39:08 GMT 024 · Counting totient values up to x gets an exact leading formula, and doubling x doubles the count in the limit. https://closedform.nishachay.tech/e/openai-math-2026-024/ https://closedform.nishachay.tech/e/openai-math-2026-024/ Wed, 14 Oct 2026 14:39:08 GMT 023 · Cubic Gauss sums over primes lean positive at exactly the rate Patterson predicted in 1978. https://closedform.nishachay.tech/e/openai-math-2026-023/ https://closedform.nishachay.tech/e/openai-math-2026-023/ Wed, 14 Oct 2026 14:39:08 GMT 022 · For any fixed shift, a weighted sum decides whether almost every number is well approximated. https://closedform.nishachay.tech/e/openai-math-2026-022/ https://closedform.nishachay.tech/e/openai-math-2026-022/ Wed, 14 Oct 2026 14:39:08 GMT 021 · Every run of about k² whole numbers holds one sharing no factor with a number that has k prime factors. https://closedform.nishachay.tech/e/openai-math-2026-021/ https://closedform.nishachay.tech/e/openai-math-2026-021/ Wed, 14 Oct 2026 14:39:08 GMT 020 · Whole-number quartics like n⁴ + 2 take squarefree values at exactly the share the local guess predicts. https://closedform.nishachay.tech/e/openai-math-2026-020/ https://closedform.nishachay.tech/e/openai-math-2026-020/ Wed, 14 Oct 2026 14:39:08 GMT 019 · Points on p-adic curves of genus two or more are claimed to match exactly the sections of their fundamental group. https://closedform.nishachay.tech/e/openai-math-2026-019/ https://closedform.nishachay.tech/e/openai-math-2026-019/ Wed, 14 Oct 2026 14:39:08 GMT 018 · Normal subgroups of these simple groups over any global field are claimed to come from finitely many local pieces. https://closedform.nishachay.tech/e/openai-math-2026-018/ https://closedform.nishachay.tech/e/openai-math-2026-018/ Wed, 14 Oct 2026 14:39:08 GMT 017 · Fractions can never get unusually close to π. https://closedform.nishachay.tech/e/openai-math-2026-017/ https://closedform.nishachay.tech/e/openai-math-2026-017/ Wed, 14 Oct 2026 14:39:08 GMT 016 · Unlikely intersections in abelian varieties are claimed to be finite in number, in every dimension. https://closedform.nishachay.tech/e/openai-math-2026-016/ https://closedform.nishachay.tech/e/openai-math-2026-016/ Wed, 14 Oct 2026 14:39:08 GMT 015 · Number-field grids spread evenly over all grid shapes in prime degrees from five, and in degrees four and six. https://closedform.nishachay.tech/e/openai-math-2026-015/ https://closedform.nishachay.tech/e/openai-math-2026-015/ Wed, 14 Oct 2026 14:39:08 GMT 014 · Linked papers claim the restricted geometric Langlands equivalence in characteristic p, plus Ramanujan bounds. https://closedform.nishachay.tech/e/openai-math-2026-014/ https://closedform.nishachay.tech/e/openai-math-2026-014/ Wed, 14 Oct 2026 14:39:08 GMT 013 · The primes cannot be built by adding two sets of whole numbers. https://closedform.nishachay.tech/e/openai-math-2026-013/ https://closedform.nishachay.tech/e/openai-math-2026-013/ Wed, 14 Oct 2026 14:39:08 GMT 012 · The largest prime factors of n and n + 1 act like independent dice, so each wins half the time. https://closedform.nishachay.tech/e/openai-math-2026-012/ https://closedform.nishachay.tech/e/openai-math-2026-012/ Wed, 14 Oct 2026 14:39:08 GMT 011 · The prime factors of p − 1, for a random prime p, are claimed to split like a randomly broken stick. https://closedform.nishachay.tech/e/openai-math-2026-011/ https://closedform.nishachay.tech/e/openai-math-2026-011/ Wed, 14 Oct 2026 14:39:08 GMT 010 · Odd two-dimensional 2-adic Galois representations are claimed to come from modular forms, with no condition mod 2. https://closedform.nishachay.tech/e/openai-math-2026-010/ https://closedform.nishachay.tech/e/openai-math-2026-010/ Wed, 14 Oct 2026 14:39:08 GMT 009 · A field of functions can be rebuilt from its multiplication, blurred by powers, plus one trace of addition. https://closedform.nishachay.tech/e/openai-math-2026-009/ https://closedform.nishachay.tech/e/openai-math-2026-009/ Wed, 14 Oct 2026 14:39:08 GMT 008 · A short list of braid equations has exactly the solutions Deligne and Drinfeld predicted, in every size. https://closedform.nishachay.tech/e/openai-math-2026-008/ https://closedform.nishachay.tech/e/openai-math-2026-008/ Wed, 14 Oct 2026 14:39:08 GMT 007 · Neighboring numbers stop agreeing on prime-factor parity. https://closedform.nishachay.tech/e/openai-math-2026-007/ https://closedform.nishachay.tech/e/openai-math-2026-007/ Wed, 14 Oct 2026 14:39:08 GMT 006 · Among the quadratic twists of any elliptic curve, half are claimed to have analytic rank 0 and half rank 1. https://closedform.nishachay.tech/e/openai-math-2026-006/ https://closedform.nishachay.tech/e/openai-math-2026-006/ Wed, 14 Oct 2026 14:39:08 GMT 005 · Catalan's constant, 1 − 1/9 + 1/25 − 1/49 + …, is not a fraction. https://closedform.nishachay.tech/e/openai-math-2026-005/ https://closedform.nishachay.tech/e/openai-math-2026-005/ Wed, 14 Oct 2026 14:39:08 GMT 004 · No algorithm can decide whether a whole-number polynomial equation has a solution in fractions, the paper claims. https://closedform.nishachay.tech/e/openai-math-2026-004/ https://closedform.nishachay.tech/e/openai-math-2026-004/ Wed, 14 Oct 2026 14:39:08 GMT 003 · No zero of Riemann's zeta function, or of any Dirichlet L-function, lies to the right of real part 7/8. https://closedform.nishachay.tech/e/openai-math-2026-003/ https://closedform.nishachay.tech/e/openai-math-2026-003/ Wed, 14 Oct 2026 14:39:08 GMT 002 · The full Birch–Swinnerton-Dyer formula is claimed for every elliptic curve with a small Selmer group at one prime. https://closedform.nishachay.tech/e/openai-math-2026-002/ https://closedform.nishachay.tech/e/openai-math-2026-002/ Wed, 14 Oct 2026 14:39:08 GMT 001 · After reduction mod p, Hodge classes on abelian varieties are claimed to give one rational number in every cohomology. https://closedform.nishachay.tech/e/openai-math-2026-001/ https://closedform.nishachay.tech/e/openai-math-2026-001/ Wed, 14 Oct 2026 14:39:08 GMT