CONTAINING CASCADING AI ERRORS: A SPECTRAL BRANCHING- PROCESS FRAMEWORK FOR VERIFICATION ALLOCATION IN MULTI-AGENT SYSTEMS

Multi-agent artificial intelligence systems can transform local model errors into networked reliability failures because one agent's output may become another agent's premise, tool input, or execution trigger.Existing work identifies hallucination propagation, task-verification failures, and runtime-assurance needs, but lacks a compact system-level threshold for deciding when error propagation becomes self-sustaining and how limited verification resources should be allocated.This paper models multi-agent error transmission as a multi-type branching process with a nonnegative next-generation matrix.It defines the cascade reproduction number, 𝑅 𝑐 = 𝜌(𝐊), and derives verification sensitivities from Perron-Frobenius theory.A two-stage Spectral Risk Verification Allocation (SRVA) policy first drives 𝑅 𝑐 below a safety margin and then minimizes expected consequence-weighted loss.In 180 synthetic 30-role systems spanning random, modular, and scale-free topologies, SRVA reduced mean post-allocation 𝑅 𝑐 to 0.737, achieved 100% stabilization, and lowered 12-generation severity loss by 43.4% relative to a static spectral baseline at equal budget.Monte Carlo stress tests also reduced catastrophic cascades from 13.67% under uniform verification to 1.00%.The framework provides a mathematically interpretable method for topology-aware assurance in agentic workflows.