# Global Coherence: When Every Agent Is Right and the Team Is Still Wrong - A Local-to-Global Semantic Foundation for Multi-Agent Collaboration

arXiv: https://arxiv.org/abs/2610.02036 · HTML: https://mlsanity.com/paper/2610.02036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 88 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [τ2-Bench: Evaluating Conversational Agents in a Dual-Control Environment](https://mlsanity.com/paper/2506.07982/) (2025)
- [A Mathematical Theory of Co-Design](https://mlsanity.com/paper/1512.08055/) (2015)
- [Sheaf theory: from deep geometry to deep learning](https://mlsanity.com/paper/2502.15476/) (2025)
- [TeamBench: Evaluating Agent Coordination under Enforced Role Separation](https://mlsanity.com/paper/2605.07073/) (2026)
- [Hypergraph Categories](https://mlsanity.com/paper/1806.08304/) (2018)

## Abstract (arXiv)

AI agents can each make locally valid decisions yet jointly produce an invalid result. We call this the global coherence problem: a failure of shared state, not merely of intelligence. Our Observation-Aliasing Impossibility Theorem gives the exact boundary. A policy can guarantee a valid action exactly when all worlds producing the same observation share an admissible action. If k indistinguishable worlds require pairwise-disjoint actions, the best randomized worst-case success is 1/k; more reasoning, roles, messages, or samples cannot recover the missing distinction. A stronger model can reason better within its context, but it cannot see beyond it. The smallest sufficient context is NP-hard to find, yet counterexample-guided refinement finds a sufficient one and recertifies it as rules change. We give local-to-global runtime semantics X = (H, C, G, F; D): topology H records overlapping scopes; category C governs state-changing actions; groupoid G keeps reversible translations; sheaf F tests whether local views glue into one world; and history D keeps only what alters legal futures. Each preserves the needed information as state is split, translated, or changed. Models propose; the harness owns shared state and governs commit. Ten studies test the boundary. On a revision benchmark, a frontier model scores 40/40 when the deciding event is visible; hidden, every arm is consistent with chance (1/3); one restored fact returns 40/40. On TeamBench, ordinary teams exceed a shared budget in 5/5 runs, a visible live count leaves 4/5, and commit enforcement leaves 0/5. In tau2-bench Telecom, current-state checks score 0.07 after silent reverts; the harness scores 1.00. Refinement keeps a sufficient context through rule changes at 28% of the all-field cost. Solvers that already own the state tie it, as predicted. Local intelligence cannot substitute for missing global state.