Banger paper from Google on agent harnesses for long-horizon tasks.

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Google Research built a many-agent harness for long mathematical proofs, and it produced new results on open problems from FOCS and JMLR papers.

Stellar Colosseum works in stages.

It explores several proof strategies, waits for a readiness gate before breaking a route into section-level subproblems, and sends each verifier finding back to the section it affects.

Inside each stage, candidates are generated in parallel, attacked with targeted falsification, and merged together with their critiques.

With Gemini 3.1 Pro and Gemini 3.7 Flash it reaches 71.0% on TCS-Bench, a set of research-level theorem-proving tasks from FOCS, STOC and SODA papers. With execution feedback it solves 218 of 222 Codeforces problems.

Paper: https://arxiv.org/abs/2609.15983

Chat with Paper: https://academy.dair.ai/papers/stellar-colosseum-a-many-agent-harness-for-long-horizon-research-in-mathematics-2609.15983