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EVIDENCE REGISTER
A chronological register of published signals. Source class, verification state, evidence quality and relevance remain visible before interpretation.
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.
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.
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 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.
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.
Ouyang, Spector and Stockdale prove a dimension-free weak-type (1,1) bound with constant 2 for the vector Riesz transform, settling Stein’s 1986 ICM problem. The paper states that the proof strategy was developed through LLM dialogues involving GPT-5.6 Sol, OpenAI reasoning agents and Claude Opus 5.0; the authors then independently checked, rewrote and validated the argument.
Avik Chakravarty, Daebeom Choi and Shengjing Xu construct counterexamples disproving Sato's weak F-equivalence conjecture for nonsingular projective toric weak Fano varieties in every dimension at least three, then formulate a Gorenstein refinement. The paper states that the results were developed with assistance from GPT-5.6 Sol.
Anthropic reports that Claude autonomously orchestrated open-source protein-design and folding tools from a human-written research prompt and produced binders against 14 of 15 targets. Adaptyv Bio and Twist Bioscience independently synthesized and tested the designs; reported hit rates were 22–35%, above the 10–15% field baseline cited by Anthropic.
The Find-Attempt-Recommend pipeline scans thousands of combinatorics papers, identifies thousands of apparently open conjectures, surfaces hundreds of potential resolutions, and narrows them to a small expert-review set. This is a material AI-for-Science signal because it automates problem selection and triage, two human bottlenecks in research-level mathematics.
A new preprint claims a full proof of Talagrand's 1989 convolution conjecture on the Boolean hypercube. The authors state that the proof was discovered by the Odin Automatic AI Research Agent; they reorganized the final proofs. Independent mathematical review is still pending.
Nam Q. Le, Qi Sun and Hung V. Tran construct uniformly elliptic nondivergence-form equations in dimension three whose bounded solutions have unbounded W1,1 variation, showing that no interior W1,p estimate depending only on ellipticity exists for p at least one and resolving negatively an open question raised by Nadirashvili, Tkachev and Vlăduţ. The authors state that the main results were obtained through chats with ChatGPT 5.6 Sol and that key strategies came from ChatGPT; they then reworked, rewrote and checked all arguments. The result remains without independent external proof reproduction.
A human-AI research collaboration tightened both lower and upper bounds on the Grothendieck constant. The companion methodology paper states that the AI system discovered and first proved the new lower bound K_G >= 6π/11, later independently checked and revised by the human authors; the exact value of K_G remains open.
A Claude-assisted research workflow reportedly improved the proportion of non-trivial simple zeros shown to lie on the critical line from about 41.6% to 67.2%. This was a substantial partial result, not a proof of the Riemann Hypothesis. The work used roughly 31M output tokens, about 60 sub-agents, around 650 discarded strategies, thousands of computational checks and Lean formalization.
The 7 August Pulse recorded WeatherNext Cyclones as roughly one day of additional warning and about a decade of meteorological progress, without a documented ASI forecast revision.
Shuoxing Zhou constructs non-isomorphic ICC property-(T) groups with isomorphic group von Neumann algebras, giving a counterexample to Connes' rigidity conjecture for this class. The paper explicitly says the result was obtained with GPT-5.6 Sol assistance, independently of and concurrently with OpenAI work. The theorem and provenance are primary-source confirmed; independent specialist verification remains pending.
Astra/OpenAI was recorded in the original Pulse as producing 10 mathematical results formalized in Lean, triggering the largest early ASI forecast revision in the archive.
Microsoft Research, Providence and University of Washington report two open-weight pathology foundation models for population-scale research. GigaPath-Flash retains 97% of GigaPath's average slide-level performance with roughly 50 times less compute. GigaTIME-Flash reports sixfold higher speed and eightfold lower memory while matching or improving spatial-protein prediction across tested cohorts.
A preprint attributed by its submitter to ChatGPT 5.6 proves full replica symmetry breaking for the zero-field Sherrington–Kirkpatrick model at zero temperature. A catalog audit found that the accompanying Lean development is conditional on seven identified analytic inputs and is not an assumption-free verification.