17 Sept 2026AI for Science
GPT-6 Astra-assisted proof settles strong secretary conjecture for linear matroids
Bérczi, Dughmi, Livanos, Soto and Verdugo prove a 1/e guarantee for the matroid secretary problem on linear matroids and state that the main proof was obtained in a conversation with ChatGPT-6 Astra. A separately authored concurrent preprint by Abdi, Banihashem, Hajiaghayi and Mittal independently proves the same linear-matroid result via an essentially identical approach.
INDEPENDENTLY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.8/10evidence 96/100
17 Sept 2026AI for Science
GPT-6 Astra-assisted proof establishes expectation form of BHM conjecture
Yinfeng Zhu proves that paths maximize the expected range of integer-valued graph homomorphisms among connected bipartite graphs of fixed order, establishing the expectation form of the Benjamini-Häggström-Mossel conjecture and deriving the Loebl-Nešetřil-Reed conjecture as a corollary. The author states that the proof was obtained through interaction with GPT-6 Astra and that the main results were formalized and checked in Lean 4.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.8/10evidence 94/100
17 Sept 2026AI for Science
GPT-5.6 Sol Ultra-assisted work sharpens trickle-down spectral-gap theorem
Xiaoyu Chen and Kuikui Liu give streamlined Bochner-method proofs of trickle-down spectral-gap results and quantitatively strengthen the Leake-Oveis Gharan theorem, resolving an open question. They state that the proofs were developed through interaction with GPT-5.6 Sol Ultra and note that Guo and Zhang independently obtained the same strengthening with a very similar argument, also found using GPT-5.6 Sol Ultra.
INDEPENDENTLY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.7/10evidence 95/100
17 Sept 2026AI for Science
Claude optimizes more than 30 open-source biomolecular models
Anthropic reports that Claude, supervised by two technical staff, optimized more than 30 open-source models across structure prediction, protein design, protein language modeling and genomics in under four weeks, averaging roughly 4x speed-ups with minimal precision loss and creating a low-memory mode for much larger biomolecular systems. Optimized code was released publicly.
PRIMARY CONFIRMEDANTHROPIC — HOW CLAUDE IS UPLIFTING BIOMOLECULAR MODELINGPrimary source ↗ Relevance8.9/10evidence 86/100
16 Sept 2026AI for Science
ChatGPT 5.6 Sol finds proofs for stronger Gorenstein-polytope decomposition results
Johannes Knupfer and Benjamin Nill prove a free-join decomposition theorem for Gorenstein polytopes that significantly strengthens prior work and prove the expected-degree characterization of the stringy E-polynomial, resolving a conjecture of Batyrev and Nill. The authors state that proofs of the general results were found via ChatGPT 5.6 Sol, while an extremal case had a prior human proof.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.6/10evidence 91/100
16 Sept 2026AI for Science
GPT-5.6 Sol-assisted work establishes degree-free spectral independence for log-concave Holant measures
Xiaoyu Chen, Zejia Chen and Xinyuan Zhang establish a degree-independent spectral-independence bound for log-concave Holant problems and derive improved Glauber-dynamics relaxation bounds. The authors explicitly state that the main proof ideas were found using GPT-5.6 Sol.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.6/10evidence 92/100
16 Sept 2026AI for Science
ChatGPT-6 Astra assists counterexample to proposed relay-channel capacity characterization
Chun Hei Michael Shiu constructs a binary relay-channel counterexample whose achievable scheme exceeds a recently proposed capacity characterization, disproving that characterization for general relay channels. The paper explicitly states that the counterexample was obtained with assistance from ChatGPT-6 Astra and that the proofs were simplified through human effort.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.1/10evidence 89/100
16 Sept 2026AI for Science
ChatGPT 5.6-assisted work improves register-program bounds for catalytic computing
Antoine Vinciguerra proves the optimality of four input accesses for passive-output register programs of degree greater than three and constructs improved four-access register programs using fewer registers, yielding improved catalytic-streaming and matrix-powering trade-offs. The paper states that generalizing the lower-bound methods and constructing the uniform family were developed with assistance from ChatGPT 5.6.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.5/10evidence 92/100
15 Sept 2026AI for ScienceBreakthrough
Independent mathematicians present GPT-6 Astra proof of the Erdős–Sós conjecture
Oliver Riordan and Alex Scott state that the Erdős–Sós conjecture was recently proved by GPT-6 Astra using a surprising argument and publish a simplified version, also determining extremal graphs and proving a related conjecture. David R. Wood separately publishes an exposition of the proof, likewise attributing its discovery to GPT-6 Astra. The multiple expert rewrites provide unusually strong independent validation of the AI-origin claim.
INDEPENDENTLY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.9/10evidence 97/100
15 Sept 2026AI for Science
ChatGPT 5.6 Sol-assisted work resolves cluster-deletion complexity question
Nicola Galesi, Tony Huynh, Arnaud Patey and Fariba Ranjbar prove Cluster Deletion is NP-complete on permutation graphs, answering an open question of Konstantinidis and Papadopoulos. The authors state that Patey found the proof with help from ChatGPT 5.6 Sol; the model-generated proof contained errors and was completely rewritten by the authors.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.5/10evidence 87/100
14 Sept 2026AI for ScienceBreakthrough
ChatGPT 6 Astra supplies key strategies resolving 2D Le simplex conjecture
Chong Gu proves that triangles minimize the Monge–Ampère eigenvalue among bounded planar convex domains of fixed area, resolving the two-dimensional case of Le's simplex conjecture. The author states that the main results were obtained through a series of chats with ChatGPT 6 Astra and that the key strategies came from the model, after which he reworked and rewrote the article.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.3/10evidence 90/100
13 Sept 2026AI for ScienceBreakthrough
GPT-5.6 Pro-assisted proof closes Ryser (4,2) case
Patrick White proves that every 4-partite 4-uniform hypergraph with matching number two has vertex-cover number at most six, confirming Tuza's unpublished 1979 claim and closing the (r,ν)=(4,2) case of Ryser's conjecture. The author reports the proof was found through four rounds of GPT-5.6 Pro and that structural claims were checked by exact MILP and brute-force computation.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.2/10evidence 94/100
12 Sept 2026AI for ScienceBreakthrough
GPT-6 Astra-assisted proof settles Conway subprime-closure growth conjecture
Romain Popescu proves that the growth ratio of Conway's subprime closure converges to the golden ratio, settling the conjecture of Caragiu, Vicol and Zaki. The paper states that the underlying proof was constructed with algorithmic assistance from GPT-6 Astra and that its correctness was formally verified in Lean 4.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.0/10evidence 94/100
12 Sept 2026AI for Science
GPT-6 Astra assists simplified proof of Rockafellar sum-conjecture failure
Radu Ioan Bot presents a simplified counterexample to Rockafellar's sum conjecture on a concrete Banach-space setting, building on a construction of Weifeng Yang. The paper says the example was developed with GPT-6 Astra assistance and explicitly cautions that it is a simplification and explanation, not an independent counterexample mechanism.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance7.8/10evidence 86/100
11 Sept 2026AI for ScienceBreakthrough
ChatGPT Sol 5.6 supplies core proof work settling undecidability of Medvedev logic
Rodrigo Nicolau Almeida and Søren Brinck Knudstorp prove Medvedev's logic of finite problems is undecidable, settling a longstanding open problem, and obtain related results for Skvortsov's logic. The paper states that the core idea and technical work of the undecidability proof were obtained using ChatGPT Sol 5.6 and formally verified in Lean by Claude Opus 5.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.5/10evidence 95/100
10 Sept 2026AI for ScienceBreakthrough
GPT-6 Astra-obtained proof settles core existence in approval-based committee elections
Patrick Becker, Matthias Greger and Dominik Peters prove that every approval-based multiwinner election admits a core-stable committee and that a Hare-core committee can be found in polynomial time, settling a central open question in the field. The arXiv record explicitly states that the proof was obtained with GPT-6 Astra. The paper also points to a Lean formalization of the core-existence theorem. This provides strong artifact-level support, but the result remains a new author-controlled preprint without independent external expert reproduction.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.5/10evidence 94/100
10 Sept 2026AI for ScienceBreakthrough
GPT-6 Astra obtains counterexample disproving the wrapping number conjecture
Qiuyu Ren exhibits an annular knot with wrapping number four whose Kauffman bracket has annular degree at most two, disproving the wrapping number conjecture. The arXiv comments explicitly state that the main result was obtained by GPT-6 Astra. The theorem and provenance are primary-source confirmed, but the four-page preprint has not yet received independent expert verification or reproduction.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.3/10evidence 87/100
10 Sept 2026AI for ScienceBreakthrough
ChatGPT Pro 6.0-assisted paper settles a conjecture on II1 factors of Fuchsian groups
Dimitri Shlyakhtenko proves that the von Neumann algebra of the fundamental group of any closed orientable surface of genus at least two is a free group factor, and extends the conclusion to arbitrary finitely generated torsion-free non-elementary discrete subgroups of PSL2(R), settling a conjecture of de la Harpe and Voiculescu. The arXiv abstract explicitly states that the result was obtained using OpenAI's ChatGPT Pro 6.0. The mathematical claim and AI-role attribution are primary-source confirmed, but the proof is a new preprint without independent expert reproduction or peer review.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.3/10evidence 88/100
09 Sept 2026AI for ScienceBreakthrough
LLM-assisted example resolves zero-private-capacity superactivation problem
Chengkai Zhu and Xin Wang resolve a longstanding quantum-information question by constructing two channels that each have zero private capacity but jointly achieve positive private communication. The paper states that the initial activation example was identified through interactions with large language models and that the result has been formalized in Lean 4. The theorem has strong author-provided formal-verification support but has not yet been independently externally reproduced.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.5/10evidence 94/100
09 Sept 2026AI for ScienceBreakthrough
Multi-model AI setup finds counterexample to the Pierce-Birkhoff conjecture
Zehua Lai, Lek-Heng Lim and Junyu Ren provide a counterexample to the Pierce-Birkhoff conjecture using a continuous piecewise-quadratic semialgebraic function that cannot be expressed as a finite lattice combination of polynomials. The arXiv abstract explicitly states that the counterexample was found with a multi-agent, multi-model setup chaining GPT 5.6, GPT 6, Claude Opus 5 and Claude Fable 5.1. The result is primary-source confirmed but not independently reproduced or peer reviewed.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.7/10evidence 88/100
08 Sept 2026AI for Science
Claude Fable 5.1 finds proof improving chromatic bound for graphs with no long induced path
Sang-il Oum improves the classical exponential chromatic bound for P_t-free graphs for t at least five, replacing the previous base t-2 with a strictly smaller asymptotic base. The paper states that the proof, a refinement of the Gyárfás path argument, was found by Anthropic's Claude Fable 5.1. The theorem and provenance are primary-source confirmed but have not yet been independently externally verified.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.8/10evidence 87/100
08 Sept 2026AI for ScienceBreakthrough
ChatGPT Astra finds initial proof resolving approval-voting complexity question
Chris Dong proves that computing a committee satisfying both justified representation and Pareto optimality is NP-hard on the unrestricted approval-profile domain, answering a stated open question negatively. The paper says an initial proof was found by ChatGPT Astra and was then verified and rewritten by the author. The result and AI provenance are primary-source confirmed; independent external proof verification is absent.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.1/10evidence 89/100
08 Sept 2026AI for Science
AI-assisted search yields counterexample answering 1992 Fibonacci multiplicative-function question
Poo-Sung Park shows that the Fibonacci numbers are not an additive uniqueness set for positive-integer-valued multiplicative functions, answering negatively a question posed by Spiro in 1992. The paper describes an AI-assisted search that led to the construction and provides a reproducible certificate checker. The mathematical claim and AI-assisted provenance are primary-source confirmed, but there is no independent external proof reproduction yet.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance8.9/10evidence 91/100
08 Sept 2026AI for ScienceBreakthrough
OpenAI multi-agent AI system produces Navier–Stokes Millennium solution
OpenAI reports that an internal model significantly more capable than GPT-6 Astra, deployed through roughly 10,000 concurrent research agents, produced an analytical proof that smooth three-dimensional Navier–Stokes dynamics can develop a finite-time singularity under the official Millennium-problem formulation. OpenAI released a proof write-up and Lean formalization. The Clay Mathematics Institute later said the problem has 'apparently been settled', while formal prize evaluation and broader community vetting remain ongoing.
INDEPENDENTLY CONFIRMEDOPENAI — ON THE NAVIER–STOKES MILLENNIUM PRIZE PROBLEMPrimary source ↗ Relevance10.0/10evidence 98/100
08 Sept 2026AI for Science
Google DeepMind launches AlphaGenome Atlas across roughly 9 billion human DNA variants
Google DeepMind launched AlphaGenome Atlas, a roughly 1-petabyte resource containing precomputed AlphaGenome predictions for the molecular effects of about 9 billion possible single-nucleotide variants across the human genome. The Atlas adds the AlphaGenome Variant Impact score to prioritize variants and is available to researchers through a web portal and API. Nature independently reported the release and quoted outside experts who describe it as useful while stressing that predictions do not replace experiments or patient-specific clinical interpretation.
INDEPENDENTLY CONFIRMEDGOOGLE DEEPMIND — ALPHAGENOME ATLAS: A PREDICTIVE MAP OF EVERY POSSIBLE DNA LETTER CHANGE IN THE HUMAN GENOMEPrimary source ↗ Relevance8.9/10evidence 96/100