arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.
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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: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.
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.
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:2607. 11307v1 Announce Type: new Abstract: Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning.
HybridProver is a unified framework that combines whole-proof synthesis and tactic-based generation using proof sketches as an intermediate representation. Implemented in Isabelle/HOL, it employs two 7B-scale LLMs trained on optimized Isabelle datasets. On the miniF2F Isabelle benchmark, HybridProver achieved a 73.8% success rate, surpassing the previous state of the art of 61.9%, and ablation studies examined the effects of dataset quality, training settings, and sampling strategies.