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:2608.28639v1 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. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.
Large language models (LLMs) have achieved remarkable performance on high-school and olympiad-style mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed.
arXiv:2608. 09277v1 Announce Type: new Abstract: Verified code generation asks a large language model (LLM) to generate both an executable program and a machine-checkable proof that the program meets a formal specification, promising software that is correct by construction.
arXiv:2607. 06447v1 Announce Type: new Abstract: Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems.
arXiv:2608. 20153v1 Announce Type: new Abstract: Large language models (LLMs) have shown growing potential for automated theoretical computer science (TCS) research, yet existing benchmarks remain far from realistic research settings.
arXiv:2606. 09450v1 Announce Type: new Abstract: LLMs have recently achieved strong results on formal proving benchmarks.
arXiv:2603. 02668v2 Announce Type: replace Abstract: We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub.
arXiv:2606. 15258v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly capable of mathematical problem solving and can even assist with research-level proofs, yet we still lack a scalable and reproducible way to measure step-level reasoning in long proofs across diverse sources.
Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules. Whether such an output that appears creative is truly original and effective is hard to establis...
arXiv:2606. 28841v1 Announce Type: cross Abstract: Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify.
LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments.