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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 Lean 4 development resolves the first question of Erdős Problem #501 as independent of ZFC: CH gives a negative model, while adding sufficiently many random reals gives a positive model. The missing large-cardinal-free transfer is credited to Elliot Glazer working with Sol and Claude; prior components were human results.
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.
Haruhisa Enomoto reports a research collaboration with Fable 5 and GPT-5.6 Sol that proposes a quotient–submodule equidistribution conjecture and proves multiple nontrivial families, with a full Lean 4 formalization. This is evidence of frontier models participating in novel mathematical research, but it does not close a pre-existing named open problem.
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.
Inherent reports that Faraday, a 27B AI Scientist agent trained with long-horizon RL and using coding agents as tools, outperforms Claude Opus 4.8 and GPT-5.5 on held-out scientific paper-replication tasks in the new 310-task Replica benchmark. The result is first-party and benchmark/judge design is controlled by the same team, so independent replication remains pending.
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.
GPT-5.6 Sol Ultra reportedly carried a Dittert-5 candidate through problem selection, discovery, certificate generation, Lean formalization, verification and manuscript preparation. The workflow was unusually autonomous, but independent human audit and review were still missing.
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.
Lorist, Meyries and Veraar construct a bounded strongly stable C0-semigroup generator on a Hilbert space whose inverse does not generate a C0-semigroup, resolving the inverse generator problem negatively. The current arXiv v2 AI disclosure states that ChatGPT 5.6 Pro explored Schauder-basis counterexamples, assisted the explicit basis construction in Proposition 2.1, and helped optimize constants.
The 6 August Pulse included a rank-3 K-U-M result recorded as Lean-verified. It was notable but did not justify an ASI forecast change.
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.
Levent Alpöge announced an explicit polynomial self-map of C^3 with constant nonzero Jacobian determinant that is not injective, refuting the Jacobian Conjecture for dimensions n≥3. Alpöge explicitly credited Claude Fable 5 with work leading to the counterexample. The result was rapidly independently checked in exact arithmetic and formally verified in Isabelle/HOL and Lean-derived work. The two-dimensional case remains open.
Colin Defant's revised paper on the MacNeille completion of Bruhat order proves a conjecture of Escobar, Klein and Weigandt and gives a counterexample to a conjecture of Hamaker and Reiner. The abstract states that those two results were obtained autonomously by ChatGPT 5.4 Pro and presents the paper as a case study in LLM-automated mathematical research. The underlying paper was first submitted in May and revised September 6; the recovered revision is primary-source confirmed but not independently externally reproduced.