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

Abstract: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 model 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. We then 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 retains reversible translations; sheaf F tests whether local views glue into one world; and minimal history D keeps only distinctions that alter legal futures. Models propose; the harness owns shared state and governs commit. Nine studies test both the failure and its boundary. On a controlled revision benchmark, the same frontier model scores 40/40 when the deciding event is visible; when it is hidden, tested arms score 12--17/40, consistent with chance (1/3); restoring one authoritative fact returns 40/40. On TeamBench, ordinary teams exceed a shared budget in 5/5 runs, a visible live count leaves 4/5 violations, and commit enforcement leaves 0/5. In tau2-bench Telecom, current-state checks score 0.07 after silent reverts, while the harness scores 1.00. Where a conventional solver already owns the complete relevant state, it ties the harness as predicted. The counterintuitive conclusion is that local intelligence cannot substitute for missing global state.

Artificial Intelligence (cs.AI)

arXiv:2610.02036 [cs.AI]

(or arXiv:2610.02036v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.02036 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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