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:2608.28639v1 Announce Type: new Abstract: Formal theorem proving with large language models remains challenging due to the difficulty of navigating large proof search spaces efficiently. Existi...
arXiv:2605. 24033v2 Announce Type: replace Abstract: Mechanistic interpretability typically discovers circuits and then argues what they do from examples and ablations.
arXiv:2609.21190v1 Announce Type: cross Abstract: Ensuring the correctness of LLM-generated code is a core challenge for modern software engineering. Benchmarks for agentic code generation check corr...
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.
Stellar Colosseum is a model‑agnostic harness designed to improve long‑horizon research in mathematics and theoretical computer science by allocating inference across multiple agents. It explores alternative strategies before constructing proofs, uses a readiness gate to decide when a route is mature enough to decompose, represents proof plans as interdependent subproblems, and routes verifier findings back to the relevant part of the argument. The workflow generates candidates in parallel, attacks them with targeted falsification, and combines candidates and critiques into a single research artifact through overlapping random‑sample tree aggregation, and has been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. Demonstrations show that, when paired with Gemini 3.1 Pro, Stellar Colosseum achieves 71.0% accuracy on the TCS‑Bench theorem‑proving benchmark and solves 218 of 222 Codeforces problems.
arXiv:2608.21356v1 Announce Type: cross Abstract: For sixty years, machine verification has been a major cost overhead, affordable only for exceptional artifacts. Here we report that generative AI in...
arXiv:2609.16302v1 Announce Type: cross Abstract: When a coding agent returns to existing software, it inherits evidence from earlier engineering work: tests, type checks, proofs, static analyses, an...
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. 05420v1 Announce Type: cross Abstract: Large language models (LLMs) can generate text that resembles a mathematical proof, but resemblance does not establish correctness.
arXiv:2607. 17047v1 Announce Type: cross Abstract: LLM constraint reasoners are often evaluated near the random-SAT phase transition, confounding density and solver hardness.
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:2609.06036v1 Announce Type: new Abstract: Proposal-based controllers---learned policies, language-model planners, and other black-box \emph{generators}---are increasingly deployed behind runtim...