A weekly roundup of curated AI progress across all topics.
115 records · Includes focused interests · How we rate progress
Alpöge and Furman report an unconditional lower bound of 0.6725 for the proportion of nontrivial zeta zeros that are simple and lie on the critical line.
Original report: 2026-08-10OpenAI claims disappearance of infinite bond-percolation clusters at criticality on every infinite connected locally finite quasi-transitive graph whose critical threshold is below one.
Read original source Pinned primary manuscript · family 213github.com
Original report: 2026-10-06Parisi and Zamponi give an analytic proof of a+b=1 from the scaling full replica-symmetry-breaking equations for infinite-dimensional hard-sphere jamming. Together with the earlier relation b=(1+c)/2, it yields the scaling identities linking force, gap and overlap exponents.
Read original source Parisi–Zamponi: precise identity, assumptions and AI disclosurearxiv.org
Original report: 2026-06-02Alpöge and Howell report elliptic curves over the rationals with at least 30 and at least 31 independent rational points of infinite order. Dujella’s specialist table records the rank-at-least-31 example as the current record, and the news account attributes assistance to an internal Claude model.
Read original source Original rank-at-least-31 record, point data and attributionelliptic-rank.icarm.cloud
Original report: 2026-08-23Math, Inc. reports Lean formalizations of sphere-packing optimality for the E₈ lattice in dimension eight and the Leech lattice in dimension 24, with uniqueness among periodic packings in dimension 24. The human maintainers report checking definitions, axiom dependencies and the supplied code.
Read original source Math, Inc.: reported formalization and scopemath.inc
Original report: 2026-03-02The pinned Anthropic development reports θ(p_c)=0 for nearest-neighbour Bernoulli bond percolation on Zᵈ in every integer dimension d≥2. It proves Kozma–Nitzan’s Conjecture 3 through an additive gluing inequality and formalizes the reduction to the lattice statement.
Read original source Pinned Anthropic development: exact lattice statementgithub.com
Original report: 2026-08-28The Alpöge–Claude manuscript claims a compact complex threefold, obtained by completing a modular family of complex two-tori, whose underlying smooth manifold is diffeomorphic to S⁶. Philip Engel supplies a separate geometric exposition and self-contained proof of the construction.
Read original source Original Alpöge–Claude constructionalpo.ge
Original report: 2026-08-23Huang, Jackson, Lee, Poonen, Pries and Zhang construct an explicit degree-23 polynomial whose splitting field over the rationals has Galois group M₂₃. They also construct a regular M₂₃ extension of Q(t), completing the realization program for all 26 sporadic finite simple groups.
Read original source Original paper v2: theorems and human/AI attributionarxiv.org
Original report: 2026-08-09Christopher D. Long reports explicit complex polynomials P and Q in three independent real Gaussian variables with E(P^m)=0 and E(QP^m)=m! for every positive integer m. A five-term degree-four example refutes the conjecture in every dimension at least three; a six-term cubic example works in four variables.
Read original source Original paper and AI-provenance sectionarxiv.org
Original report: 2026-07-20The manuscript reports one deterministic algorithm computing the exact complex discrete Fourier transform at every length n in O(n(log n)^(1−10^−13)) operations, including scalar preparation, scheduling and indexing, in its specified arithmetic model.
Read original source Pinned manuscript, Theorem 1.1 and Corollary 1.2github.com
Original report: 2026-10-06The AlphaEvolve report gives a rank-48 decomposition of the 4×4 matrix-multiplication tensor over the complex numbers, yielding a bilinear algorithm using 48 scalar multiplications.
Read original source AlphaEvolve technical report, §3.1arxiv.org
Original report: 2025-05-14For every convex body K in R^n, n≥1, the manuscript reports volume product at its Santaló point at least (n+1)^(n+1)/(n!)², with equality exactly for simplices.
Original report: 2026-10-06The manuscript reports arbitrarily large finite simple graphs with independence number at most two and chromatic number greater than their largest clique-minor order. It also claims violation of the ordinary fractional-coloring weakening.
Original report: 2026-10-06Math, Inc. reports completion of a Lean formalization of the strong prime number theorem and supporting complex-analysis infrastructure using Gauss with human guidance.
Original report: 2025-09-11Ellenberg, Libedinsky, Plaza, Simental and Williamson prove that for n=2^m, dyadically well-distributed permutations form a Bruhat interval isomorphic to a hypercube of dimension m·2^(m−1). This has order n log n, within a constant factor of the maximum.
Read original source Original paper, Theorem 1.1 and methodologyarxiv.org
Original report: 2026-01-03DeepMind reports AI-discovered assembly sorting routines translated to C++ and incorporated in LLVM libc++. Its tests report up to 70% improvement for length-five inputs and about 1.7% for inputs exceeding 250,000 elements.
Original report: 2023-06-07Akhil Mathew’s contribution gives a noncommutative finite free group scheme of order four over a nonreduced base that is not killed by four.
Read original source Mathew’s statement and AI disclosuregithub.com
Original report: 2026-07-14Alpöge and Buckmaster report finite-time blowup for the inviscid Boussinesq equations on R² with smooth spatially compact forcing in both equations. Temperature remains bounded, while its gradient and the vorticity become unbounded.
Read original source Alpöge–Buckmaster manuscript and AI statementcims.nyu.edu
Original report: 2026-09-07The manuscript reports smooth compactly supported divergence-free initial data on R³ whose unforced three-dimensional incompressible Euler solution has finite maximal lifespan, with unbounded velocity gradient and divergent time integral of maximum vorticity.
Read original source Original Euler manuscript, Theorem 1.1cdn.openai.com
Original report: 2026-09-08For every positive viscosity, the manuscript reports a three-dimensional incompressible Navier–Stokes flow starting from rest with smooth compactly supported forcing, bounded kinetic energy, and unbounded velocity in finite time. It claims Clay alternatives C on R³ and D on the periodic torus.
Read original source Original manuscript, Theorem 1.1cdn.openai.com
Original report: 2026-09-08OpenAI reports that rational Hodge classes on abelian varieties with good reduction pair rationally with complementary divisor products on the reduction, compatibly across prime-to-p and crystalline realizations, including residue characteristic two.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports the complete Birch–Swinnerton-Dyer leading-term formula for elliptic curves over the rationals whose full q-power Selmer group has corank zero or one at some prime q, including all local prime factors.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that no algorithm can decide whether an integer-coefficient polynomial has a rational solution when the number of variables is part of the input.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that, for each elliptic curve over the rationals, its quadratic twists of analytic rank zero and one each have density one half among signed squarefree parameters ordered by absolute value.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports cancellation with a power-of-logarithm saving for ordinary two-point Liouville averages along fixed nonproportional affine forms, and a binary corrected Elliott result under uniform nonpretentiousness.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that the rational Grothendieck–Teichmüller Lie algebra is free on one generator in each odd weight starting at three, with the corresponding weight-completed isomorphism.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that no set differing from the positive primes at finitely many integers is a sumset A+B of two nonnegative-integer sets that each contain at least two elements.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that divergence of the totient-weighted approximation sum gives infinitely many successful shifted approximations for almost every real number, for each fixed real shift and arbitrary finite-valued tolerances.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports at least c_a x/(log x)² primes in each sufficiently large interval (x,2x) for which a fixed integer a is a primitive root, whenever a is neither minus one nor a square.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports modularity of every elliptic curve over every imaginary quadratic number field, with an automorphic representation matching the local parameters at all places.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that K_X+mL is globally generated on every smooth complex projective n-dimensional variety for every ample line bundle L and every integer m at least n+1.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that, at r at least ten very general complex plane points, the total multiplicity of every nonzero effective degree-d curve is strictly less than d times the square root of r.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports area-integrability of the s-th power of the derivative of every conformal bijection from a simply connected planar domain to the unit disk whenever 4/3<s<4, together with the stated inverse-square integral-means exponent.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every compact subset of Euclidean d-space, d at least two, with Hausdorff dimension strictly greater than d/2 has a distance set of positive Lebesgue measure.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports the three-dimensional Kakeya maximal L³ estimate with tube-radius loss at most C_ε δ^(-ε) for every positive ε, uniformly over unit tubes of radius δ.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every origin-symmetric convex body in n-dimensional real space has volume product at least 4^n/n!, with equality precisely for invertible linear images of Hanner polytopes.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that the sum of squared Gaussian first-moment lengths of the cells of every finite measurable Euclidean partition is at most 9/(8π), with the three-sector planar construction attaining the bound in the stated dimensions.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports a deterministic polynomial-time reduction from 3SAT to fixed-alphabet Unique Games with completeness at least 1−ε and soundness at most δ for each fixed ε,δ in (0,1/2).
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports a uniform deterministic logarithmic-space simulation of polynomial-time randomized logarithmic-space decision procedures with bounded error, yielding L=RL=BPL.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports randomized k-server competitive ratio O(log²(k+1)) on every metric against oblivious requests, matching the stated worst-case lower-bound order; distinct initial server positions need no additive term.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports uniform deterministic complete factorization of a densely represented polynomial over a binary-specified prime field in bit complexity polynomial in (degree+1) log p, including irreducible factors and multiplicities.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every positive-integer set with divergent reciprocal sum contains arithmetic progressions of every finite length, through fixed-length bounds r_k(N)≤C_k N exp(−c_k(log N)^ε_k).
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports a bipartite graph with 35 vertices and 66 edges whose homomorphism density in a finite simple host is below the predicted edge-density bound; it also reports failure of the associated forcing assertion.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every nonempty finite oriented graph has a vertex with at least as many vertices at directed distance exactly two as at directed distance one.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports a finitely presented torsion-free group with a finite two-dimensional classifying space whose group algebra over the two-element field contains nonzero elements with product zero.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports a finitely presented torsion-free group with a finite two-dimensional classifying complex and elements a,b in its characteristic-two group algebra satisfying ab=1 but ba≠1.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports one fixed finite-dimensional complex algebra with finite-dimensional modules of unbounded finite projective dimension, refuting universal finiteness of little finitistic dimension.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports a nondegenerate limiting law for centered and variance-normalized total free energy in the zero-field Gaussian Ising Sherrington–Kirkpatrick model at each fixed β>1, with variance asymptotic to a positive constant times n^(1/3).
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every order automorphism of the full Turing-degree partial order is the identity in ZFC, without a definability or regularity restriction on the automorphism.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that consistency of ZF implies consistency of ZF plus the Partition Principle and Choice for ordinal-indexed families but without the full Axiom of Choice.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports an infinite discrete group with an ordinary finite presentation that is residually finite and has finite two-power order for every element, with unbounded element orders.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that Thompson’s group F, viewed as a discrete group, is nonamenable.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports purely absolutely continuous spectrum of nonzero weight on an open energy interval for the lattice Anderson model with independent uniform site potentials at each fixed dimension d≥3 and sufficiently small positive disorder.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that the maximum number of mutually unbiased orthonormal bases in complex dimension six is three, using an exhaustive computer-assisted exclusion of four bases under specified arithmetic and compiler conditions.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports a uniform positive spectral gap above the ground energy for the pure antiferromagnetic spin-one Heisenberg chain on even periodic rings.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every bounded complex-linear unital homomorphism from a unital complex C*-algebra to operators on a Hilbert space is conjugate by a bounded invertible operator to a *-homomorphism.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports vanishing of universal-cover L²-Betti numbers outside degree two for closed connected aspherical topological four-manifolds, and more generally finite aspherical integral Poincaré complexes of formal dimension four.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports the generalized Cartan–Hadamard isoperimetric inequality in every dimension for complete simply connected smooth manifolds with sectional curvature at most κ≤0, comparing finite-volume finite-perimeter sets with equal-volume model balls.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every complete connected noncompact Kähler manifold with strictly positive holomorphic bisectional curvature is biholomorphic to complex Euclidean space.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06OpenAI reports that every nonzero first-positive Neumann eigenfunction on a smooth bounded simply connected planar domain has nonvanishing interior gradient, placing all global extrema on the boundary even for a multiple eigenvalue.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06Alman and Vassilevska Williams report deterministic O(n^1.9992) 3SUM on polynomial-size integers and O(n^2.9995) APSP with polynomially bounded integer weights in the word-RAM model.
Read original source Alman–Vassilevska Williams: algorithms and methodologyarxiv.org
Original report: 2026-10-05Flake, Gruber and Heidersdorf report that the universal rigid monoidal category on one object has an abelian envelope without the quotient property.
Original report: 2026-09-15Almeida and Knudstorp report that Medvedev’s logic of finite problems is undecidable, by reducing periodic plane tiling to non-theoremhood.
Original report: 2026-09-11Coester, Koutsoupias and Zbysiński report that the work function algorithm is k-competitive on every metric space.
Original report: 2026-09-14The artifact reports exact optimal radii and classifications of optimal packings for one through seven freely rotated unit squares in a disk.
Read original source Original researchgithub.com
Original report: 2026-10-02The artifact reports (3,4,5,20,22,36) schedulable but (3,4,5,20,22,32) unschedulable, refuting the proposed six-task kernel cap.
Read original source Original researchgithub.com
Original report: 2026-09-30Braun reports more than exp(n/(32768ℓ²)) clauses for DAG-like Res(⊕) refutations of the bit pigeonhole principle, for n=2^ℓ and ℓ≥32, without depth or regularity restrictions.
Original report: 2026-09-19Becker, Greger and Peters report that every approval-based multiwinner election has a core committee and that one can be found in polynomial time.
Original report: 2026-09-10Kerger reports Ω(d²/log(d+1)) exact-function-value queries at accuracy Θ(d^−1/2) for deterministic convex Lipschitz minimization over a d-dimensional ball.
Original report: 2026-07-14The Ulam writeup reports a polynomial map C³→C³ with constant nonzero Jacobian determinant −2 and three distinct points sharing one image.
Original report: 2026-07-20The AFP development records a seven-vertex instance with fractional cost 58 but unsplittable cost at least 60, even allowing additive congestion 15.
Read original source Original researchisa-afp.org
Original report: 2026-07-22The human-verified writeup gives a fixed ε>0 and growing planar point sets with at least n^(1+ε) unit distances.
Original report: 2026-05-20Dupont and collaborators report ω<2.371177 by improving the combination-loss optimization and refining it with AlphaEvolve.
Original report: 2026-08-17OpenAI claims globally smooth unique evolution for arbitrary admissible large initial data in the three-dimensional one-species relativistic Vlasov–Maxwell model, under its support and field assumptions.
Read original source Pinned primary manuscript · family 362github.com
Original report: 2026-10-06OpenAI claims that every compact boundaryless smooth Riemannian surface has a smooth length-preserving immersion into R⁴, including nonorientable surfaces.
Read original source Pinned primary manuscript · family 333github.com
Original report: 2026-10-06OpenAI reports the sharp constant-two numerical-range inequality for matrix-valued polynomials, uniformly over all finite base and coefficient dimensions.
Read original source Pinned primary manuscript · family 325github.com
Original report: 2026-10-06OpenAI claims Lie-group structure for any locally compact second-countable Hausdorff group with a faithful jointly continuous action on a connected finite-dimensional manifold under the stated topological conventions.
Read original source Pinned primary manuscript · family 304github.com
Original report: 2026-10-06OpenAI claims a normal trace-preserving *-isomorphism between the free group factors L(F₂) and L(F₃), giving the affirmative branch of the classical isomorphism alternative.
Read original source Pinned primary manuscript · family 287github.com
Original report: 2026-10-06OpenAI reports the sharp invariant-mass lower bound in terms of minimum enclosing area for one-ended spacetime initial-data exteriors in every dimension n≥3, under the paper’s energy, trapping and decay assumptions.
Read original source Pinned primary manuscript · family 260github.com
Original report: 2026-10-06OpenAI claims that a hyperbolic group with a two-sphere boundary has a proper cocompact action by isometries on hyperbolic three-space, allowing a finite kernel.
Read original source Pinned primary manuscript · family 246github.com
Original report: 2026-10-06OpenAI claims that every infinite Löwenheim–Skolem bound admits a uniform threshold above which one categorical cardinal forces categoricity throughout the remaining tail, in ZFC.
Read original source Pinned primary manuscript · family 240github.com
Original report: 2026-10-06OpenAI claims strict positivity of the Tor Euler characteristic for nonzero finite modules of complementary dimension over a regular local ring, when their tensor product has finite length.
Read original source Pinned primary manuscript · family 193github.com
Original report: 2026-10-06OpenAI claims a finite degree-dependent upper bound for the total number of isolated periodic trajectories of any planar polynomial vector field.
Read original source Pinned primary manuscript · family 143github.com
Original report: 2026-10-06OpenAI claims a conformal circle-domain model for an arbitrary planar domain, allowing uncountably many complementary components.
Read original source Pinned primary manuscript · family 071github.com
Original report: 2026-10-06OpenAI claims that rational Hodge classes on any complex CM abelian variety admit algebraic-cycle representatives with rational coefficients, in all codimensions.
Read original source Pinned primary manuscript · family 032github.com
Original report: 2026-10-06OpenAI’s manuscript reports that all Dirichlet L-functions and finite-order Hecke L-functions over Q(√−3) have no zeros with real part greater than 7/8.
Read original source Original manuscript · family 003github.com
Original report: 2026-10-06The manuscript reports a proof that Catalan’s constant is irrational.
Read original source Original manuscript · family 005github.com
Original report: 2026-10-06The manuscript reports that the irrationality exponent of π equals 2.
Read original source Original manuscript · family 017github.com
Original report: 2026-10-06The manuscript reports h(k) ≪ k²/(log log(3k))², answering the quadratic-bound question in its stated formulation.
Read original source Original manuscript · family 021github.com
Original report: 2026-10-06The manuscript reports that every a/b with 1 ≤ a < b and sufficiently large b has an expansion with O(log log b) distinct positive unit fractions.
Read original source Original manuscript · family 025github.com
Original report: 2026-10-06The manuscript reports a uniform finite bound on component size for every fixed step limit in the Gaussian-prime graph.
Read original source Original manuscript · family 028github.com
Original report: 2026-10-06The manuscript reports an L₁ embedding with a universal distortion bound for every finite connected planar graph with positive real edge lengths.
Read original source Original manuscript · family 089github.com
Original report: 2026-10-06The manuscript reports density at most C n log n for a single-lattice covering by translates of every convex body in dimension n ≥ 2.
Read original source Original manuscript · family 092github.com
Original report: 2026-10-06The manuscript reports matching bounds exp(Θ(√(log d · log log d))) for the least ℓ₁ distortion of unit-cost edit distance on strings of length at most d.
Read original source Original manuscript · family 099github.com
Original report: 2026-10-06The manuscript reports a deterministic quasipolynomial algorithm for the nonnegative-value vertices of finite turn-based stochastic mean-payoff games.
Read original source Original manuscript · family 104github.com
Original report: 2026-10-06The manuscript reports that the complex matrix-multiplication exponent is at most 9/4.
Read original source Original manuscript · family 107github.com
Original report: 2026-10-06The manuscript reports deterministic multiplication in O(n (log n)^(1−κ)) time with κ = 2^−182 on a fixed finite-tape Turing machine.
Read original source Original manuscript · family 109github.com
Original report: 2026-10-06The manuscript reports arbitrarily large additive configuration-LP gaps and additive-approximation hardness for rational item sizes greater than 1/6.
Read original source Original manuscript · family 118github.com
Original report: 2026-10-06The manuscript reports a randomized algorithm taking (n+m)^(1+o(1)) time and returning a maximum matching with probability at least 2/3.
Read original source Original manuscript · family 120github.com
Original report: 2026-10-06The manuscript reports a randomized (1+ε)-approximation in N^(1+o(1)) worst-case expected time for each fixed rational ε in (0,1).
Read original source Original manuscript · family 121github.com
Original report: 2026-10-06The manuscript reports a deterministic polynomial-time algorithm producing a common superstring of length at most twice optimum.
Read original source Original manuscript · family 128github.com
Original report: 2026-10-06The manuscript reports a randomized classical Subset Sum algorithm in O(2^(0.49n)) time for polynomial-bit inputs.
Read original source Original manuscript · family 138github.com
Original report: 2026-10-06The manuscript reports a nine-dimensional counterexample using rank-one orthogonal projectors on R⁴ with the Frobenius metric.
Read original source Original manuscript · family 156github.com
Original report: 2026-10-06The manuscript reports that five colors cannot suffice, implying that the plane’s chromatic number is six or seven if the result holds.
Read original source Original manuscript · family 158github.com
Original report: 2026-10-06The manuscript reports R(5,t) = t⁴/(log t)^(3+o(1)) as t tends to infinity.
Read original source Original manuscript · family 170github.com
Original report: 2026-10-06Anthropic reports an end-to-end Lean proof of Fermat’s Last Theorem and makes the formal development and verification instructions available.
Read original source Original announcementanthropic.com
Original report: 2026-09-04Sothanaphan’s writeup reports infinitely many factorial-divisibility triples with a+b−n in any prescribed positive logarithmic window, while a and b remain bounded away from 0 and n.
Read original source Sothanaphan’s theorem and writeuparxiv.org
Original report: 2026-01-12The authors report configurations packing 11 and 12 unit regular hexagons inside regular hexagons of approximate side lengths 3.931 and 3.942, respectively.
Read original source Georgiev, Gómez-Serrano, Tao, and Wagner paperarxiv.org
Original report: 2025-11-03The authors report new infinite families attaining R(B(n−1), B(n)) = 4n−1 for specified parameters, where B(k) is k triangles sharing an edge.
Original report: 2026-08-24The September 2026 preprint reports three exact 604-point configurations in eleven dimensions.
Original report: 2026-08-24AlphaEvolve’s authors report an eleven-dimensional kissing configuration with 593 outer spheres.
Original report: 2025-05-14DeepMind reports Lean proofs for IMO 2024 problems 1, 2, and 6, and publishes the specific proof artifacts.
Read original source Original report (25 July 2024)deepmind.google
Original report: 2024-07-25The authors report packing heuristics that outperform tested baselines on their online one-dimensional bin-packing experiments.
Original report: 2023-12-14The FunSearch paper reports new large cap-set constructions improving the authors’ stated finite-dimensional and asymptotic baselines.
Original report: 2023-12-14The authors report an algorithm multiplying 4×4 matrices over the two-element field using 47 scalar multiplications, compared with 49 from two levels of Strassen’s algorithm.
Original report: 2022-10-05A weekly roundup of curated AI progress across all topics. No specific interests required.
The weekly update gathers newly published contributions and relevant changes across the entire catalog. Each record retains its original sources, verification evidence, and limitations.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
Claude: a reported improvement in the proportion of zeta zeros on the critical line
OpenAI reports: Critical percolation on quasi-transitive graphs
Parisi–Zamponi–Claude: an analytic proof of the jamming exponent identity
Alpöge–Howell–Claude: elliptic curves of rank at least 30 and 31
Gauss: AI-assisted sphere-packing formalization in dimensions 8 and 24
Claude reports: no infinite critical cluster on integer lattices
Alpöge–Claude reports: a complex structure on the six-sphere
AI-assisted realization of the Mathieu group M₂₃ over the rationals
AI-assisted small counterexamples to the Gaussian Moments Conjecture
OpenAI reports: a power saving for exact discrete Fourier transforms
OpenAI reports: Mahler’s conjecture for general convex bodies
Gauss: AI-assisted strong prime number theorem formalization
AI-assisted counterexample to Grothendieck’s group-scheme question
OpenAI reports: Strict hot spots on simply connected planar domains
OpenAI reports: An infinite finitely presented residually finite 2-group
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