{
  "schema_version": 1,
  "verified_on": "2026-08-23",
  "verifier": "scripts/verify-conformal-bootstrap-certificate.mjs",
  "certificate_sha256": "25d2c0ba27675101f249645ac67e70a1db2725d01a89b188b097cdcd50fc0bc8",
  "verification_result_sha256": "237dfc99a5de97404c5cb2ab66b5c307ca2ade9bd259fcffdece61613c59a4b1",
  "negative_controls_rejected": 3,
  "verified_quantities": {
    "fixture_id": "qft.fixture.conformal-bootstrap.rational-half-line-certificate",
    "result": "pass",
    "arithmetic": "exact rational using normalized BigInt numerator-denominator pairs",
    "feasible_control_residual": [
      "0",
      "0",
      "0"
    ],
    "finite_generator_actions": [
      "1",
      "0",
      "1"
    ],
    "excluded_target_action": "-1",
    "generator_polynomial_coefficients": [
      "1",
      "-2",
      "1"
    ],
    "gram_polynomial_coefficients": [
      "1",
      "-2",
      "1"
    ],
    "gram_principal_minors": [
      "1",
      "1",
      "0"
    ],
    "continuum_identity": "alpha(v(x)) = (x - 1)^2 >= 0 for every x >= 0",
    "cft_identity_action": "1",
    "cft_k_polynomial_coefficients": [
      "133/8",
      "8",
      "1"
    ],
    "cft_p_polynomial_coefficients": [
      "11",
      "133/3",
      "64/3",
      "8/3"
    ],
    "cft_k_gram_principal_minors": [
      "133/8",
      "1",
      "133/8",
      "8"
    ],
    "cft_p_gram_principal_minors": [
      "11",
      "64/3",
      "704/3",
      "133/3",
      "8/3",
      "1064/9"
    ],
    "cft_analytic_input": "For Delta > 0, g_Delta(1/2) > 0 and r_Delta = g_Delta'(1/2)/g_Delta(1/2) >= 8 Delta/3.",
    "cft_claim_ceiling": "Together with the stated analytic positivity input, the exact rational data exclude a nonidentity gap Delta >= 9/2 in the declared reflection-positive one-dimensional crossing problem. They do not validate a generic block approximation or a solver implementation.",
    "claim_ceiling": "This certificate excludes one target from the declared toy half-line moment cone. It is not a conformal-field-theory bound."
  }
}