An isomorphism of the free group factors
- Mathematics
OpenAI 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.
Archive
1033 matching entries · Page 21 of 21
The spacetime Penrose inequality and enclosing area
- Mathematics
- Theoretical Physics
OpenAI 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.
A Modulus Proof of Cannon’s Conjecture
- Mathematics
OpenAI 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.
Eventual categoricity for abstract elementary classes
- Mathematics
- Theoretical Computer Science
OpenAI claims that every infinite Löwenheim–Skolem bound admits a uniform threshold above which one categorical cardinal forces categoricity throughout the remaining tail, in ZFC.
Positivity of Serre's Intersection Multiplicity
- Mathematics
OpenAI 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.
Uniform bounds for planar polynomial limit cycles
- Mathematics
OpenAI claims a finite degree-dependent upper bound for the total number of isolated periodic trajectories of any planar polynomial vector field.
Koebe's Circle-Domain Conjecture
- Mathematics
OpenAI claims a conformal circle-domain model for an arbitrary planar domain, allowing uncountably many complementary components.
The rational Hodge conjecture for CM abelian varieties
- Mathematics
OpenAI claims that rational Hodge classes on any complex CM abelian variety admit algebraic-cycle representatives with rational coefficients, in all codimensions.
Catalan's constant is irrational
- Mathematics
The manuscript reports a proof that Catalan’s constant is irrational.
The irrationality exponent of pi is 2
- Mathematics
The manuscript reports that the irrationality exponent of π equals 2.
A quadratic bound for Jacobsthal's function
- Mathematics
The manuscript reports h(k) ≪ k²/(log log(3k))², answering the quadratic-bound question in its stated formulation.
Bounded-Step Walks on Gaussian Primes
- Mathematics
The manuscript reports a uniform finite bound on component size for every fixed step limit in the Gaussian-prime graph.
Planar Graph Metrics Embed into L1 with Constant Distortion
- Mathematics
The manuscript reports an L₁ embedding with a universal distortion bound for every finite connected planar graph with positive real edge lengths.
A single-lattice covering bound of order n log n
- Mathematics
The manuscript reports density at most C n log n for a single-lattice covering by translates of every convex body in dimension n ≥ 2.
Edit Distance in l1: Matching Bounds up to Constants in the Exponent
- Mathematics
The 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.
Turn-Based Stochastic Mean-Payoff Games in Deterministic Quasipolynomial Time
- Mathematics
- Theoretical Computer Science
The manuscript reports a deterministic quasipolynomial algorithm for the nonnegative-value vertices of finite turn-based stochastic mean-payoff games.
Integer multiplication below n log n
- Mathematics
- Theoretical Computer Science
The manuscript reports deterministic multiplication in O(n (log n)^(1−κ)) time with κ = 2^−182 on a fixed finite-tape Turing machine.
Additive hardness and unbounded configuration gaps in bin packing
- Mathematics
- Theoretical Computer Science
The manuscript reports arbitrarily large additive configuration-LP gaps and additive-approximation hardness for rational item sizes greater than 1/6.
Almost-Linear-Time Maximum-Cardinality Matching in General Graphs
- Mathematics
- Theoretical Computer Science
The manuscript reports a randomized algorithm taking (n+m)^(1+o(1)) time and returning a maximum matching with probability at least 2/3.
An Almost-Linear Approximation Scheme for Edit Distance
- Mathematics
- Theoretical Computer Science
The manuscript reports a randomized (1+ε)-approximation in N^(1+o(1)) worst-case expected time for each fixed rational ε in (0,1).
A Polynomial-Time 2-Approximation for Shortest Common Superstring
- Mathematics
- Theoretical Computer Science
The manuscript reports a deterministic polynomial-time algorithm producing a common superstring of length at most twice optimum.
Subset Sum in Time O(2^{0.49n})
- Mathematics
- Theoretical Computer Science
The manuscript reports a randomized classical Subset Sum algorithm in O(2^(0.49n)) time for polynomial-bit inputs.
A nine-dimensional counterexample to Borsuk's covering assertion
- Mathematics
The manuscript reports a nine-dimensional counterexample using rank-one orthogonal projectors on R⁴ with the Frobenius metric.
The Euclidean plane is not five-colorable
- Mathematics
The manuscript reports that five colors cannot suffice, implying that the plane’s chromatic number is six or seven if the result holds.
The sharp logarithmic exponent of r(5,t)
- Mathematics
The manuscript reports R(5,t) = t⁴/(log t)^(3+o(1)) as t tends to infinity.
Resolution of Erdős Problem #728: a writeup of Aristotle's Lean proof
- Mathematics
- Theoretical Computer Science
The original clarified Erdős #728 factorial-divisibility solution obtained by GPT-5.2 Pro and Aristotle; later sharpness and strengthened corollaries in v5 are separate human/model follow-ups.
Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment
- Mathematics
Station v2 Section 6.13 S1: a conference graph with parameters (q,(q-1)/2,(q-5)/4,(q-1)/4) gives R(B_q,B_(q+1))=4q+3. S2: every prime power Q>3 with Q=3 mod 8 gives R(B_((Q-1)/2),B_((Q+1)/2))=2Q+1. Exclude the third Yamada–Pott family requiring human expert synthesis.
Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment
- Mathematics
The three exact model-generated 604-point kissing configurations in dimension 11 in Station v2 Section 6.3. Two are reported as new isometry classes; the overlapping concurrent construction does not establish sole AI priority.
AlphaEvolve: A coding agent for scientific and algorithmic discovery
- Mathematics
AlphaEvolve’s authors report an eleven-dimensional kissing configuration with 593 outer spheres.
Olympiad-level formal mathematical reasoning with reinforcement learning
- Mathematics
- Theoretical Computer Science
DeepMind reports Lean proofs for IMO 2024 problems 1, 2, and 6, and publishes the specific proof artifacts.
Mathematical discoveries from program search with large language models
- Mathematics
- Theoretical Computer Science
The authors report packing heuristics that outperform tested baselines on their online one-dimensional bin-packing experiments.
Mathematical discoveries from program search with large language models
- Mathematics
The FunSearch paper reports new large cap-set constructions improving the authors’ stated finite-dimensional and asymptotic baselines.
Discovering faster matrix multiplication algorithms with reinforcement learning
- Mathematics
- Theoretical Computer Science
The 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.
Considered but not curated
These entries have recorded screening decisions and are not counted as curated contributions. Importance, evidence, interest, and date filters apply only to curated contributions.
View all matching screening decisionsSource freshness
These dates show source checks, not the latest research. Failed checks can leave gaps.
arXiv · algebra-geometry — last successful metadata check: 21/10/2026, 07:20:46 UTC
arXiv · algorithms-formal — last successful metadata check: 21/10/2026, 07:19:48 UTC
arXiv · analysis — last successful metadata check: 21/10/2026, 07:21:51 UTC
arXiv · combinatorics — last successful metadata check: 21/10/2026, 07:18:49 UTC
arXiv · geometry-topology — last successful metadata check: 21/10/2026, 07:22:23 UTC
arXiv · logic-foundations — last successful metadata check: 21/10/2026, 07:23:04 UTC
arXiv · optimization-information — last successful metadata check: 21/10/2026, 07:23:10 UTC
arXiv · probability-dynamics-physics — last successful metadata check: 21/10/2026, 07:22:36 UTC
arXiv · theoretical-physics — last successful metadata check: 21/10/2026, 07:22:50 UTC