# Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science

arXiv: https://arxiv.org/abs/2609.15983 · HTML: https://mlsanity.com/paper/2609.15983/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 46 of its 68 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 30 of 46)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Competitive Programming with Large Reasoning Models](https://mlsanity.com/paper/2502.06807/) (2025)
- [CodeElo: Benchmarking Competition-level Code Generation of LLMs with Human-comparable Elo Ratings](https://mlsanity.com/paper/2501.01257/) (2025)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [LiveCodeBench Pro: How Do Olympiad Medalists Judge LLMs in Competitive Programming?](https://mlsanity.com/paper/2506.11928/) (2025)
- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [Accelerating Scientific Research with Gemini: Case Studies and Common Techniques](https://mlsanity.com/paper/2602.03837/) (2026)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [Advancing Mathematics Research with AI-Driven Formal Proof Search](https://mlsanity.com/paper/2605.22763/) (2026)
- [AI co-mathematician: Accelerating mathematicians with agentic AI](https://mlsanity.com/paper/2605.06651/) (2026)
- [QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems](https://mlsanity.com/paper/2604.24021/) (2026)
- [LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization](https://mlsanity.com/paper/2606.05400/) (2026)
- [Sparse Convex Optimization via Adaptively Regularized Hard Thresholding](https://mlsanity.com/paper/2006.14571/) (2020)
- [Harnessing the Collective Intelligence of AI Agents in the Wild for New Discoveries](https://mlsanity.com/paper/2606.10402/) (2026)
- [Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models](https://mlsanity.com/paper/2602.16793/) (2026)
- [Aletheia tackles FirstProof autonomously](https://mlsanity.com/paper/2602.21201/) (2026)
- [Provable Quantization with Randomized Hadamard Transform](https://mlsanity.com/paper/2605.13810/) (2026)
- [Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory](https://mlsanity.com/paper/2607.06447/) (2026)
- [Can Language Models Falsify? Evaluating Algorithmic Reasoning with Counterexample Creation](https://mlsanity.com/paper/2502.19414/) (2025)
- [RMA: an Agentic System for Research-Level Mathematical Problems](https://mlsanity.com/paper/2605.22875/) (2026)
- [ProofCouncil: An LLM Agent for Solving Open Mathematical Problems](https://mlsanity.com/paper/2607.09474/) (2026)

## Built on by (most cited first, 1 of 1)

- [Optimal and Efficient Online Inverse Optimization](https://mlsanity.com/paper/2610.08735/) (2026)

## Abstract (arXiv)

Language models can produce plausible short proofs, but may still be unreliable on long-horizon research problems, where progress depends on a sequence of uncertain and interdependent decisions. We introduce Stellar Colosseum, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science. Colosseum explores alternative strategies before proof construction, uses a readiness gate to decide when a route is mature enough to decompose, represents the proof plan as interdependent section-level subproblems, and routes verifier findings back to the affected part of the argument. Across these stages, it generates candidates in parallel, attacks them with targeted falsification, and combines candidates and their critiques into a single research artifact through overlapping random-sample tree aggregation. The Colosseum workflow has been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. We demonstrate the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks. Using Colosseum with Gemini 3.1 Pro, we obtain several new results that address open problems arising from papers published at top venues such as FOCS and JMLR. On TCS-Bench, a benchmark of research-level theorem-proving tasks drawn from papers published at FOCS, STOC, and SODA, Colosseum achieves 71.0% accuracy using Gemini 3.1 Pro and Gemini 3.7 Flash. In a separate Codeforces evaluation using Gemini 3.1 Pro, the proof-oriented pipeline with execution feedback solves 218 of 222 problems.