arXiv:2608.28997v1 Announce Type: new Abstract: In May 2026 an OpenAI model produced a counterexample to the Erd\H{o}s unit distance conjecture. Five mathematicians published a human-verified version...
arXiv:2607. 25637v1 Announce Type: cross Abstract: F(AI)2R is FAIR research with AI in the loop, twice: an AI-assisted authoring pass and a machine-readable audit pass over every artefact.
arXiv:2607. 06341v1 Announce Type: cross Abstract: Formal verification offers the strongest guarantee of software correctness, but it does not scale: the proofs demanded by interactive theorem provers such as Coq require enormous expert effort.
arXiv:2606. 26057v1 Announce Type: cross Abstract: AI agents are granted access to tools, APIs, and other infrastructure, making them active principals in those systems.
arXiv:2607. 12650v1 Announce Type: cross Abstract: Tool access alone does not make LLM empirical reasoning governable: accepted outputs need not descend from attested evidence, and accepted deductions need not hold up under formal scrutiny.
arXiv:2607. 01223v1 Announce Type: new Abstract: When should an AI system's answer be trusted?
VeriPhy is an auditable physical‑verification system that transforms a text prompt into typed physical obligations and a statically validated execution plan before any video frames are generated. During execution, it gates calls to frozen low‑level experts (segmentation, tracking, counting, depth, OCR, audio‑event detection, etc.) and records provenance‑carrying evidence for each action. The system maps these records to a three‑valued state—supported, contradicted, or unknown—providing traceable verdicts that can be used to refine generation models.
arXiv:2606. 05400v1 Announce Type: cross Abstract: Long-horizon autoformalization of research mathematics fails not only at hard lemmas, but at scale: statements drift, dependencies tangle, context decays, and local repairs corrupt distant work.
Formal verification offers the strongest guarantee of software correctness, but it does not scale: the proofs demanded by interactive theorem provers such as Coq require enormous expert effort. Large language models (LLMs) promise to generate these proofs automatically, yet existing approaches wire a fixed, human-designed proof strategy into the system and constrain the model to follow it (retrieving premises and predicting tactics one step at a time, or splitting goals by divide-and-conquer), and still prove only a fraction of their target theorems.
arXiv:2608. 12700v1 Announce Type: new Abstract: Systems that generate GPU kernels with language models report high correctness rates.
The paper addresses the asymmetry in verifying optimality claims for synthesis pipelines, distinguishing between the upper bound (existence of a program) and the lower bound (non-existence of a smaller program). It introduces a pipeline that synthesizes minimal linear straight‑line programs over GF(2) and produces DRAT proofs for every UNSAT result, thereby closing the so‑called refutation gap for 121 previously uncertified optimality claims. The authors report that the median proof size is 1.1 MB, checking takes 1.9× the solving time, and that their verification process uncovered defects missed by code review, highlighted interface obstacles, and exposed a budget‑related audit failure.
arXiv:2607. 14340v1 Announce Type: cross Abstract: AI coding agents produce code faster than humans can review it.