Locally Coherent, Globally Incoherent: A Post-Aggregation Failure Mode in Multi-Component LLM Agents

Multi-component LLM agents (planners with tools, specialist routers, multi-stage pipelines) assemble probabilistic claims from components that each see only part of a joint problem. Each component can be locally coherent, and even individually calibrated in principle, yet the composed belief can violate basic probability axioms: marginals over complementary events sum past one; partitions exceed the unit-mass budget by more than 2×. Three intuitive mitigations (retrieval grounding, partition-aware prompting, and delegating coherentisation to an aggregator LLM) each silently fail or actively regress on a measurable fraction. We trace the failure to specialists not seeing cross-component coupling constraints, formalise it as an output-only runtime certificate, and propose a deterministic geometric repair that drives the residual to zero without an LLM call. The failure is structural: ε⋆ >0 on 33–94% of 1,876 ensemble cliques, 20/20 planner-discretion partitions, and 97.8% of 268 frontier-panel bets, translating to +0.115 nats per bet of decision-relevant regret on 1,770 resolved markets. Disclosing the constraint to specialists reduces but does not eliminate the residual. Code: https://anonymous.4open.science/r/compositional-incoherence-BEC7