{
 "what": "The registry's C_86 certificate (R. Pinho, #227, merged 2026-10-18 with an asterisk) decided by two implementations that share no code with each other or with the claimant's checker (never run): the six finite conditions E1–E6 of Smith's sufficiency criterion and the bound's arithmetic, exact where the data is rational and by sound enclosures where a logarithm enters; the step from the conditions to C_86 <= bound is the published chain (the minimum principle, Smith's criterion and theorem [Smi24]), read and not re-derived here",
 "generated": "2026-10-21T01:54:34Z",
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   "jsSeconds": 3.8,
   "fired": true,
   "py": "REFUTED",
   "pyFailed": [
    "E5"
   ],
   "pySeconds": 31.6
  },
  {
   "id": "weights-scaled-1.3",
   "what": "every weight scaled by 1.3: Σ b_Q deg Q exceeds the mass (E3)",
   "expect": "REFUTED",
   "mustFail": [
    "E3"
   ],
   "js": "REFUTED",
   "jsFailed": [
    "E3"
   ],
   "jsSeconds": 0.5,
   "fired": true,
   "py": "REFUTED",
   "pyFailed": [
    "E3"
   ],
   "pySeconds": 2
  },
  {
   "id": "extra-mass-near-0.05",
   "what": "density 1/100 added in the first cell of the support: ∫ log|x| dμ turns negative (E4) and the bound no longer matches (E6)",
   "expect": "REFUTED",
   "mustFail": [
    "E4",
    "E6"
   ],
   "js": "REFUTED",
   "jsFailed": [
    "E4",
    "E6"
   ],
   "jsSeconds": 0.5,
   "fired": true,
   "py": "REFUTED",
   "pyFailed": [
    "E4",
    "E6"
   ],
   "pySeconds": 1.6
  },
  {
   "id": "tampered-bound",
   "what": "the certificate's bound lowered by 10^-12: it no longer equals ∫ x dμ / m (E6)",
   "expect": "REFUTED",
   "mustFail": [
    "E6"
   ],
   "js": "REFUTED",
   "jsFailed": [
    "E6"
   ],
   "jsSeconds": 0.5,
   "fired": true,
   "py": "REFUTED",
   "pyFailed": [
    "E6"
   ],
   "pySeconds": 1.5
  },
  {
   "id": "reducible-polynomial",
   "what": "x^2 - 3x + 1 replaced by x^2 - 3x + 2 = (x - 1)(x - 2): not irreducible (E2)",
   "expect": "REFUTED",
   "mustFail": [
    "E2"
   ],
   "js": "REFUTED",
   "jsFailed": [
    "E2"
   ],
   "jsSeconds": 0.1,
   "fired": true,
   "py": "REFUTED",
   "pyFailed": [
    "E2"
   ],
   "pySeconds": 0.2
  },
  {
   "id": "complex-roots",
   "what": "x^2 - 3x + 1 replaced by x^2 + 1: no real root (E2)",
   "expect": "REFUTED",
   "mustFail": [
    "E2"
   ],
   "js": "REFUTED",
   "jsFailed": [
    "E2"
   ],
   "jsSeconds": 0.1,
   "fired": true,
   "py": "REFUTED",
   "pyFailed": [
    "E2"
   ],
   "pySeconds": 0.2
  }
 ],
 "limits": [
  "E5 is decided on the closed cells with positive density; the extension to C is the claimant's minimum-principle argument, read",
  "irreducibility is decided for degree <= 5 by the absence of integer roots and of monic integer quadratic factors (Mignotte bound) — every Q here is monic up to sign with constant term ±1",
  "the two deciders share the mathematics (the Taylor form on boxes) and nothing else"
 ]
}