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...
The paper introduces EasyProver, a Lean theorem prover that uses recursive agents, isolated contexts, asynchronous search, parallel tactic probing, and an elastic elaboration service. It achieves near‑saturation results on several benchmark suites, proving 669/672 PutnamBench problems, all six IMO 2026 formalizations, 597/600 NTP4VC verification conditions, and all 189 VERINA tasks. Additionally, the authors present Aegis, a pipeline that transforms competitive programming problems into harder verification tasks by generating safe Rust solutions, translating them to Lean, and producing 2,045 Rust‑Lean program pairs with 11,533 candidate specifications, enabling new benchmarks for provers and reinforcement learning.
count-catcher is a tool that transforms a CPOG certificate produced by the exact model counter d4 into a Lean theorem asserting that a CNF formula defined in Lean has exactly N models over V variables. It verifies the equivalence between the formula and a Boolean circuit via forward and reverse checks, using Lean’s LRAT checker and formally verified computations. The resulting theorems are combined with Mathlib results, such as Burnside’s lemma, to count combinatorial objects—for example, proving the number of Latin squares of order 8 as a weighted sum of certified counts from terabytes of certificates.
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.
SEVERUS is a context‑aware, gamified framework that generates Verus benchmarks by organizing verification tasks into quests and progressively removing auxiliary lemmas to create levels of increasing difficulty. It constructs 819 quests with 10,095 levels from six open‑source Rust projects, and uses an independent checker to enforce soundness while a noisy binary search estimates agent capabilities. Experiments with GPT‑6 Sol, GPT‑6 Luna, and Claude Code show that as proof context is withdrawn, success rates drop and costs rise, with the strongest agents solving only 35% of levels reliably.
arXiv:2610. 13461v1 Announce Type: new Abstract: AI systems are making rapid progress in mathematics, but this progress is hard to measure.
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.