{
  "paper": "Hordijk_Steel_Critical_Window_arxiv.pdf, September 2026",
  "seed": 20260908,
  "trials_per_point": 400,
  "python": "3.11.0",
  "numpy": "2.4.1",
  "matplotlib": "3.10.5",
  "source_sha256": "c3eeda153e9ccaf66be80ebd73ac0fb1b576cd1dd8179bff761cc58848648ada",
  "exact_history_test": {
    "matrices_checked": 64,
    "history_polynomials_equal": true,
    "individual_matrix_histories_differ": 2
  },
  "positive_bound": {
    "a": "1/2",
    "lambda": "ln(2)",
    "m": 2,
    "k": 458,
    "L": 4580,
    "exact_condition_verified": "7 * (2*7^64*81) * 3^k <= 4^k",
    "positive_lower_bound": "2^(-((4580-2)*2^(4580+1)+5))",
    "upper_bound_from_36_gateways": "1 - 2^(-36)",
    "meaning": "Bounds use Theorem 7.1 and Proposition 7.2; not a numerical estimate."
  },
  "static_barrier_check": {
    "n": 6,
    "intensity": 0.2,
    "retained_pool_size_k": 63,
    "static_openness": 0.13643167152844432,
    "trials": 400,
    "barrier_successes": 53,
    "RAF_successes": 282,
    "violations": 0,
    "scope": "Samplewise implication in canonical coupling; law transfers by Lemma 5.1."
  },
  "intervals": "Pointwise 95% Wilson; neither simultaneous nor finite-size error bounds.",
  "randomness": "NumPy default_rng, SeedSequence with documented separate spawn keys.",
  "coupling": "Common marks across intensities and static escape boundaries.",
  "limits": "No infinite survival, continuity, convergence rate or Lean proof was numerically verified."
}