{
  "path": "genesis/verify/binomial_ci.py",
  "find": "lo = 0.0 if k == 0 else float(beta.ppf(alpha / 2.0, k, n - k + 1))",
  "replace": "lo = 0.0 if k == 0 else float(beta.ppf(alpha / 2.0, k + 1, n - k + 1))",
  "why": "Shifts the lower Clopper-Pearson quantile by one success. The certificate's yield interval is then no longer the exact interval the claim promises; the gate's independent textbook recomputation disagrees beyond 1e-12 (yield_ci_matches_textbook FAIL) and the witness exits 1. It is the same designed mutation dataroom/witness_quality.json measured (exit 1)."
}