Calibration Is Not Verification: Falsifiability-Aware Conformal Routing for Mixture-of-Agents

Abstract: Multi-agent language systems often treat agreement as evidence, yet heterogeneous agents can jointly repeat an unsupported claim or omit a correct specialist fact. We introduce C-MoA, an agreement-based conformal filter that turns inter-agent semantic support into a claim-level nonconformity score and calibrates a retention threshold at the example level, giving distribution-free within-domain factuality control for heterogeneous Mixture-of-Agents. C-MoA is effective: it nearly doubles retained-claim precision on long-form generation (from 0.41 to 0.75), certifies a human-labelled medical set, and transfers across domains without recalibration; its one failure mode is short-form answering, where consensus is cheap and the score is left near chance. We then ask whether counterfactual falsifiability can push past consensus, and introduce CONTRA-MoA, which adds a blinded near-miss tournament, leave-one-agent-out stability, and availability-aware fusion. This extension helps only where the verifier holds domain knowledge, dropping half of the false medical claims at 0.940 precision, whereas with a memory-only judge the added signals are near chance (AUC 0.531 and 0.511) and naive max fusion degrades the working agreement signal from 0.687 to 0.652. The message is twofold: agreement-based conformal calibration delivers reliable, transferable factuality control, while moving beyond consensus requires a knowledgeable verifier, availability-aware signals, and robust fusion.