# Cogentic: Multi-Agent Orchestration for Automated Proof Discovery

arXiv: https://arxiv.org/abs/2609.40324 · HTML: https://mlsanity.com/paper/2609.40324/

## Key facts

- No citing papers in the map yet (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 39 of its 74 references that are in the map.
- First posted on arXiv 30 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 39)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Agent-as-a-Judge: Evaluate Agents with Agents](https://mlsanity.com/paper/2410.10934/) (2024)
- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [An AI system to help scientists write expert-level empirical software](https://mlsanity.com/paper/2509.06503/) (2025)
- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [Optimal anytime regret with two experts](https://mlsanity.com/paper/2002.08994/) (2020)
- [Contextual Recommendations and Low-Regret Cutting-Plane Algorithms](https://mlsanity.com/paper/2106.04819/) (2021)
- [A Simple and Approximately Optimal Mechanism for an Additive Buyer](https://mlsanity.com/paper/1405.6146/) (2014)
- [A Duality-Based Unified Approach to Bayesian Mechanism Design](https://mlsanity.com/paper/1812.01577/) (2018)
- [Online Inverse Linear Optimization: Efficient Logarithmic-Regret Algorithm, Robustness to Suboptimality, and Lower Bound](https://mlsanity.com/paper/2501.14349/) (2025)
- [Revisiting Online Learning Approach to Inverse Linear Optimization: A Fenchel-Young Loss Perspective and Gap-Dependent Regret Analysis](https://mlsanity.com/paper/2501.13648/) (2025)
- [Finite and Corruption-Robust Regret Bounds in Online Inverse Linear Optimization under M-Convex Action Sets](https://mlsanity.com/paper/2602.01682/) (2026)
- [Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets](https://mlsanity.com/paper/1903.06696/) (2019)
- [Continuous Prediction with Experts' Advice](https://mlsanity.com/paper/2206.00236/) (2022)
- [ProofCouncil: An LLM Agent for Solving Open Mathematical Problems](https://mlsanity.com/paper/2607.09474/) (2026)
- [Towards Minimax Online Learning with Unknown Time Horizon](https://mlsanity.com/paper/1307.8187/) (2013)
- [Auction Design in an Auto-bidding Setting: Randomization Improves Efficiency Beyond VCG](https://mlsanity.com/paper/2204.10956/) (2022)
- [Simple Projection-Free Algorithm for Contextual Recommendation with Logarithmic Regret and Robustness](https://mlsanity.com/paper/2603.20826/) (2026)
- [Multiscale Reward Hedging from Correct Demonstrations](https://mlsanity.com/paper/2608.06825/) (2026)

## Abstract (arXiv)

We present Cogentic, a multi-agent harness for automated proof discovery on open research problems. While frontier language models can generate strong mathematical ideas in a single shot, single-shot generation is often insufficient for open problems that require exploring multiple competing conjectures, overcoming subtle technical obstructions, and retaining intermediate progress over a long horizon. Cogentic addresses these challenges through an iterative prove-verify loop in which an orchestrator allocates a population of independent provers across distinct proof directions, subjects their output to adversarial verification by several specialized components, and promotes confirmed intermediate results into a persistent verified ledger that later rounds build on. The harness is designed to be able to solve research-level math and theoretical computer science problems. Using either Gemini 3.1 Pro or an early version of Gemini 4 Argon as the base model, Cogentic produced novel results on open problems across online learning, auction theory, and mechanism design. Each result was independently verified by domain experts and is developed in full in companion papers. We list these results, and new ones as they are verified, at https://sites.google.com/view/cogentic .