{
  "schema": "zerone-science-exact-check/v1",
  "pass": true,
  "review_scope": "same-operator internal check; no external review",
  "verifier_sha256": "2887b292eb073e877ae9966be6e2227b2bece460c0bf1b9ac3fa30279f80ae1d",
  "witness": {
    "fixed_points": [
      "0"
    ],
    "phi": "1",
    "b": "1/2",
    "input_distance": "1/2",
    "output_distance": "3/4",
    "ratio": "3/2",
    "global_condition": "piecewise polynomial factor certificate"
  },
  "coefficient_checks": [
    {
      "phi": "1",
      "b": "1/2",
      "decrease_coefficient": "3/4"
    },
    {
      "phi": "1",
      "b": "2",
      "decrease_coefficient": "0"
    },
    {
      "phi": "1",
      "b": "3",
      "decrease_coefficient": "-3"
    },
    {
      "phi": "4",
      "b": "1/4",
      "decrease_coefficient": "1/16"
    },
    {
      "phi": "4",
      "b": "3/4",
      "decrease_coefficient": "-3/16"
    }
  ],
  "adversarial_edges": [
    "zero b hides a nonzero original residual",
    "positive but vanishing b_n=1/n loses uniform residual control",
    "signed weights 2,-1 cancel residuals of Q1=0 and Q2=-I",
    "constant maps -1 and +1 have an averaged fixed point but no common fixed point",
    "negative generalized parameter permits cancelling residual of Q2=2I",
    "unnormalized weight 2 with constant Q=1 moves the common fixed point",
    "a(x)=min(1,|x-1|), a(1)=1: r=a*x loses demiclosedness at 1",
    "b=2/phi loses strict decrease; b>2/phi may lose quasi-nonexpansiveness"
  ],
  "projection_checks": {
    "lemma33_limsup": "1",
    "eq13_left": "1/2",
    "eq13_right": "0"
  },
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  ],
  "control_warning": "rho=1 control lies outside the printed rho interval"
}