Support-Flow Control Resists Persuasion by Echo in Fixed-Evidence Multi-Agent Debate

Multi-agent debate can corrupt its own evidential record: once a weak claim is reused as a premise, later turns amplify its authority without adding evidence. We formalize this failure as persuasion by echo and introduce support-flow control, which governs how evidential credit propagates between claims while an argument is being written. RelayGuard instantiates this principle by decomposing direct, inherited, and unsupported support, weighting unsupported reuse by downstream influence, and expiring influential claims until new evidence re-grounds them. Under matched evidence and generation budgets, RelayGuard attains a $26.7$ judge-fooled rate across three controlled tasks, versus $29.0$ for active ate-flat, $29.3$ for Answer$+$Verifier, and $29.8$ for sle-flat. The advantage extends to two fixed-corpus evaluations: RelayGuard lowers judge-fooled rate by $2.5$ points on FEVER-evidence and $2.8$ points on ContractNLI relative to Answer$+$Verifier. Together, matched controls, mechanism diagnostics, and external fixed-corpus results establish support inheritance as a controllable state of multi-agent reasoning and transcript formation as a decisive point for provenance-aware oversight.