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EVIDENCE REGISTER
A chronological register of published signals. Source class, verification state, evidence quality and relevance remain visible before interpretation.
A new preprint proves that the free Heyting algebra on two generators cannot be the lattice of subterminal objects of any elementary topos, giving a negative answer to a longstanding realization question. The authors report help from ChatGPT 5.6 Sol but retain authorship and responsibility.
A multi-university preprint reports a multi-agent system that proposed, implemented, debugged, trained and evaluated roughly 80 ESMFold-derived code variants, outperforming matched Codex-proposal and random-search controls on a development benchmark.
A Google-led preprint extends Gemini-based Co-Scientist from hypothesis generation into execution-grounded workflows spanning experiment planning, laboratory interaction, real-data validation and manuscript generation across materials science, biology and computer science.
A new arXiv preprint proves that every sufficiently large genus admits a closed hyperbolic surface with systole at least log g minus 12 log log g, improving the asymptotic lower-bound constant valid uniformly across all sufficiently large genera from 2/9 to 1. Author Yifei Cai states that the proof was developed through an extended discussion with GPT-5.6 Sol.
Google Antigravity reports seven notable mathematics and theoretical-computer-science results from Teamwork. The detailed first-party report states the seven results were obtained with Gemini 3.1 Pro and that Problems 1, 3 and 4 were independently rerun within the Teamwork system using Gemini 3.7 Flash. The same framework operates autonomously over hours or days, retains failed approaches and verifier findings across rounds, and also built a RISC-V simulator validated against external timing oracles.
A UCL-developed system analysed endoscopic video during pituitary-tumour surgery and highlighted critical anatomy in real time while the neurosurgeon retained full control; the tumour was removed and the patient’s vision improved.
An arXiv preprint constructs a real meromorphic-function counterexample that the authors describe as an independent negative answer to a question dating to Nevanlinna’s 1925 work. The paper explicitly states that the core construction and proof were generated during an autonomous run of GPT-5.6 Sol Ultra.
Version 2 of arXiv:2606.28244 adds a theorem disproving a De Giorgi conjecture for non-uniformly elliptic equations. André Guerra states that GPT-5.6 Pro generated the initial proof essentially autonomously; he then spent several days understanding and verifying it and wrote the final proof himself.
A preprint proves rapid mixing for proper colorings and broader spin systems on graphs of girth at least five near the q=(1+δ)Δ threshold; the authors say the main proof ideas were developed through interactions with GPT-5.6 Sol Ultra.
A preprint gives the first polynomial-time algorithm for stable matching in network hypergraphic preference systems; the authors say ChatGPT-5.6 Sol Max discovered the key connection, which they then verified and wrote up themselves.
An EPFL-led preprint reports a three-agent MCP framework that translates natural-language microscopy requests into checked commands, assesses AFM images, tunes bounded parameters and diagnoses artifacts across live nanoscale-characterization experiments.
Accelerated Understanding launched a neural-operator-based physical AI system that directly predicts 4D physical evolution, reports inference beyond 5 trillion context elements, training up to 1 trillion parameters and scaling tests to 35 trillion parameters.
Levent Alpoge publicly claims a construction of a complex structure on the six-sphere, a classical long-standing open problem, and attributes substantial work to Claude/Opus 5. The claim is not yet independently verified and S^6 has a history of failed claimed solutions.
Ava Howell submitted curve #302 to the NSF ICARM Elliptic Curve Rank Leaderboard with 31 explicitly exhibited independent rational points, proving rank >=31 unconditionally. The leaderboard commentary attributes the discovery to Claude, Levent Alpöge and Ava Howell. Exact rank 31 is additionally certified conditional on BSD+GRH. This advances the rank frontier but does not resolve whether elliptic-curve ranks over Q are unbounded.
Zeta Lab reports five original mathematical theorems produced during an AI-directed research pursuit, all accepted by the Lean proof kernel with no unfinished proof steps. The lab separately distinguishes its stronger zeta-zero bound as a candidate rather than a theorem.
A public AI-assisted research pipeline reports a new 67.30530% candidate lower bound for the proportion of simple zeros of the Riemann zeta function on the critical line, building on Anthropic and subsequent public certificate work. The finite certificate was verified across 64 shards, but the project explicitly states that a substantial analytic bridge remains unproved/reviewed, so the composite claim remains a candidate and does not solve the Riemann Hypothesis.
Keefer Rowan constructs the first smooth random fast dynamo on T^3. The paper states that the central proof idea was generated autonomously by ChatGPT 5.6 Sol Ultra, while the author wrote and verified the manuscript. The result is a random-flow analogue and does not fully solve the deterministic smooth fast-dynamo problem.
A 20 Aug 2026 preprint by Mian Huang, Yanxiao Liu and Yi Liu gives an unconditional counterexample showing the complete one-letter Marton region can be strictly sub-optimal. The numerical search relied heavily on GPT-5.6 Sol, Claude Fable 5 and Opus 5; the authors certify the numerical gap with exact rational arithmetic and outward-rounded MPFR.
A newly submitted curve on the iCARM Elliptic Curve Rank Leaderboard has rank at least 30, satisfying a named AIM problem that asked for an elliptic curve over Q of rank 30. The leaderboard uses exact 2-descent certification to establish independence of the exhibited rational points. Public discussion links the discovery to Levent Alpöge, Ava Howell and Claude, but the discovery method and AI contribution have not yet been documented in a primary paper, so the AI role remains unclear.
Keigo Oka gives a deterministic exact O*(1.89^n) algorithm for counting linear extensions of arbitrary n-element posets, resolving Koivisto’s 2013 Dagstuhl question. The paper disclosure says Claude Opus 5 discovered the core mathematical ideas behind the new algorithm and proof; the research prompt was generated by ChatGPT 5.6 Sol.
Édouard Bonnet proves that every sufficiently large finite planar point set has either four collinear points or six pairwise visible points, resolving the first open case of the Kára–Pór–Wood Big-Line-Big-Clique conjecture. The paper states that after a failed attempt and generic encouragement, GPT-5.6 Sol Pro produced a relatively detailed proof after 222 minutes; the author checked and simplified it and rewrote the exposition.
Shou, Gorshkov, Galitski and Miller report a complete proof of the hiding conjecture for Gaussian boson sampling with an arbitrary number of squeezed input modes. The acknowledgments explicitly state that GPT-5.5 Thinking/Pro and GPT-5.6 Sol were used to generate proof ideas and methods, with all results checked and validated by the human authors.
ManXis reports a task-conditioned meta-agent architecture that dynamically forms specialized scientific agents, completing 170/170 recursive long-horizon tasks and producing certified mathematical/theoretical outputs. The paper also reports progress on a localized Weil-positivity certificate related to the Riemann Hypothesis, explicitly stating it is not an RH proof.
Jihao Liu presents a smooth polarized projective fivefold that is K-polystable but admits no constant-scalar-curvature Kähler metric, thereby disproving the original cscK Yau–Tian–Donaldson conjecture. The paper documents that GPT-5.6 Sol, Fable 5 and Danus produced the counterexample and proof; an improved Danus run starting only from the original problem reportedly reproduced a complete solution in 5h29m without the key human intervention used in the first run.
Deep Origin reran its computational drug-discovery challenge with 2026 frontier models. The best autonomous run recovered 922/1000 hidden top structures, above the prior unrestricted human reference of 77.8%; five runs exceeded that reference. Performance is strongly harness-dependent and the public benchmark may have been exposed in training, limiting causal inference.