{
  "status": "all exact rational assertions passed",
  "scope": "identities, branch margins, sampled finite dual and cheap-prefix profiles; not a formal proof checker",
  "profiles_checked": 216,
  "old_coefficient": "8257/49923",
  "new_coefficient": "8242/49923",
  "new_coefficient_decimal": 0.16509424513751178,
  "gain": "5/16641",
  "gain_decimal": 0.00030046271257736916,
  "relative_coefficient_reduction_percent": 0.18166404263049535,
  "cap_gain": "21119/11094000",
  "outer_gains": {
    "small_rho": "2975/399384",
    "large_rho": "186/79507",
    "PF_tail": "1822061/103041072"
  },
  "original_certificate_date": "2026-10-24",
  "verification_date": "2026-11-05"
}