Provide a formal false-discovery guarantee for MCES

Prove a formal false-discovery or false-discovery-rate bound for the MCES convergence classifications, rather than relying solely on empirical false-positive measurements under the evaluated scenarios.

Background

The paper applies Benjamini–Hochberg gating to applicable per-method significance tests and reports low empirical rates of null pairs reaching Moderate-or-higher convergence. These results are explicitly limited to the evaluated synthetic and benchmark scenarios.

The authors do not derive a formal guarantee for the downstream CES thresholding and cross-method aggregation procedure. Establishing such a bound would provide theoretical error control beyond scenario-specific empirical validation.

References

We describe this as strong empirical false-positive control on the evaluated scenarios; we do not prove a formal false-discovery bound, and do not claim one.

— Multi-Method Causal Evidence Synthesis: Ranking Candidate Drivers by Convergent Cross-Method Evidence from Observational Data  (2608.20187 - Gupta et al., 20 Aug 2026) in Section 5.8, “Empirical False-Positive Behavior and Threshold Sensitivity”; Section 6.2, Limitations