代理系統與評測
Stellar Colosseum Breaks Long Proofs Into Agent Competitions, Reaching 71% on TCS-Bench With Cross-Model Selection
Google Research has unveiled Stellar Colosseum, which manages long-horizon mathematical research through strategy exploration, counterexample attacks, dependency graphs, and hierarchical aggregation. The system scored 71% on the 300-problem TCS-Bench, but the result relies on extensive inference and automated grading and should not be treated as evidence of a model’s independent proving ability.
Researchers from Google Research and Carnegie Mellon University released the [Stellar Colosseum paper](https://arxiv.org/abs/2609.15983) on September 14, seeking to address a problem in long-horizon mathematical research: early strategic mistakes contaminating every subsequent step of a proof. Rather than simply increasing the number of samples, the system first proposes multiple solution strategies in parallel and assigns each candidate a dedicated falsifier to search for counterexamples, hidden assumptions, and circular reasoning. The candidates and critiques are then synthesized layer by layer through overlapping randomized sampling trees, avoiding the need to pack every trajectory into a single context.
Once a route passes the readiness gate, the system divides the proof into chapter-level subproblems with explicit dependencies. Independent sections can be handled in parallel; when local verification fails, only the affected chapters are redone. The system returns to the exploration stage only when global verification shows that the core strategy is unworkable. Failed drafts, counterexamples, and confirmed results are written to a shared knowledge directory for reuse in later rounds. This workflow has been ported to the Long Proof pattern in [Google Antigravity Teamwork](https://antigravity.google/blog/teamwork-when-ai-becomes-a-research-partner), although the product version uses less parallelism than the paper’s case studies to control costs.
On TCS-Bench, which contains 300 research-level theorem-proving tasks, Colosseum runs using Gemini 3.1 Pro alone and Gemini 3.7 Flash alone achieved 54% and 55%, respectively. The system then had Flash generate eight critiques of each proof produced by Pro and used a five-vote threshold to select between the two candidates, raising the score to 71%. In a separate Codeforces evaluation, it passed 218 of 222 problems on the original hidden test set.
The key engineering contribution is not merely the use of “multiple agents,” but the implementation of disagreement, falsification, dependencies, and rollback as a persistent control workflow. However, final decisions on TCS-Bench are still made by a model-based grader that has access to reference proofs, and the paper does not provide enough complete data to compare costs, token usage, or wall-clock time. Future evaluation should focus on blinded review by human experts, a fully reproducible harness, and comparisons against best-of-N and single-agent long-context methods under equal budgets.