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:2607.00815v2 Announce Type: replace-cross Abstract: If the certificate produced by a SAT solver is checked by a verified checker, we get a verdict which convinces. But this verdict cannot be na...
arXiv:2607. 00815v1 Announce Type: cross Abstract: SAT solvers settle combinatorial problems beyond the reach of interactive theorem provers and produce LRAT certificates for independent verification.
SemantEq introduces a principled method for verifying that formal statements faithfully translate natural‑language mathematics by requiring each statement to transform into the other through a chain of allowed logical steps, rather than relying on trivial logical equivalence. The system evaluates proofs using Lean’s proof terms, achieving 100 % precision and 65.6 % recall on the ProofNetVerif test split, outperforming prior methods. A complementary audit tool, SemantEq‑ProofAudit, further improves recall for equivalent pairs while rejecting all non‑equivalent pairs.
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.
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:2610.17358v1 Announce Type: cross Abstract: Formal verification proves that a program satisfies its specification, but says nothing about whether the specification captures what the author mean...
Papers in statistical theory rest on long proofs that few readers check line by line. We present KAPPA (Kit of Agents for Proof-checking Papers with a proof Assistant), open-source software that organ...
KAPPA is an open‑source toolkit that uses language‑model agents to translate LaTeX proofs from statistical papers into Lean 4, where each numbered result is verified step by step against the original text. The system assigns one of four verdicts—verified unconditionally, verified conditionally, issue recorded, or unfinished—to every result, and it can run unattended, re‑check only changed sections, and report resource usage. In tests on four example papers and three published statistical papers, KAPPA detected the known errors and additional issues that were later confirmed by hand, while a direct language‑model approach without the kit produced fewer correct verdicts and sometimes over‑claimed proofs.
The paper presents a design-time verification framework for truly fearless concurrent and distributed systems. It describes a compiler that tracks wait‑for edges, preserves proofs while lowering code directly to native CPU, GPU, NPU, and FPGA targets, and uses a Program Semantic Graph to maintain the values and relationships that justify boundary contracts. Four verification tiers—structural inference, local arithmetic checks, reusable domain lemmas, and probabilistic relational proofs—enable comprehensive verification without developer annotations, supporting distributed proofs with Iris, Actris, and Aneris.
arXiv:2609.26806v2 Announce Type: replace-cross Abstract: This paper presents a complete, structure-preserving port to Lean 4 of the Isabelle/HOL dataset accompanying Benzm\"uller and Scott's study o...
arXiv:2610.08319v1 Announce Type: new Abstract: In proof assistants such as Lean, a generated proof must pass machine compilation checks, so evaluation needs no human scoring. Direct generation fails...