When Should Inference Be Split? A Fixed-Budget Theory of Predictable Multi-Agent Advantage under Local Context Ceilings

This paper develops a fixed-budget theory of when inference should be split across multiple agents rather than kept inside a single strong workspace. Many claims of multi-agent superiority are difficult to interpret because they mix unmatched compute budgets, unpaid orchestration, extra external memory, stronger verification, and weak single-agent baselines. This work separates those effects by charging worker inference, routing, communication, memory operations, and verification inside one common additive budget, while treating local context as a nonadditive per-node ceiling. The paper distinguishes three layers that are often conflated. The first is a task-level surrogate utility for exploration, coordination, and redundancy reduction. The second is a deployability layer that tracks end-to-end correctness using candidate coverage, conditional evaluation-selection accuracy, and post-selection hijack risk. The third is a structural layer that studies when an architecture can preserve or destroy critical higher-order interactions under communication and context limits. Within this framework, the paper defines matched strong single-workspace baselines, gives an exact cost-aware decomposition for the surrogate utility, formalizes measurable diagnostics for decomposability, diversity, shared-failure dependence, and communication fidelity, and separates general structural results from tractable-model propositions and proxy-certified diagnostics. The main practical question is not whether “more agents” are better in the abstract, but under what conditions splitting inference is justified. The analysis shows that multi-agent advantage depends on nonredundant search, preserved interaction structure, adequate verification strength, fair budget matching, and careful treatment of latency and external memory. The result is a design-oriented theory for AI reasoning systems, collective inference, test-time compute allocation, and reliable decision pipelines under local context ceilings.