{
  "schema": 1,
  "origin": "coordinator_exact_symbolic_checks_not_model_or_formal_certificate",
  "source_sha256": "8adb9681e2cd5e4bdcb292162a32796b00ae7b757a5a900fbd580d0bc939e34e",
  "sympy_version": "1.14.0",
  "lemma_5_2": {
    "A": [
      [
        13,
        8
      ],
      [
        8,
        5
      ]
    ],
    "B": [
      [
        13,
        -8
      ],
      [
        -8,
        5
      ]
    ],
    "complete_singular_spectra": [
      "9+4*sqrt(5)",
      "9-4*sqrt(5)"
    ],
    "all_four_forward_inverse_operator_norms": "9+4*sqrt(5)",
    "cross_inner_product_squared": "1/5 > 1/9",
    "self_inner_products": 1,
    "word": "A inverse",
    "observed_action_norm": "9-4*sqrt(5)",
    "claimed_lower_bound": "(9+4*sqrt(5))/3",
    "status": "exact_counterexample_to_native_statement"
  },
  "theorem_3_4": {
    "normalized_limiting_gap_density": "8 exp(-3y) sinh(y), y>=0",
    "tail": "2 exp(-2T)-exp(-4T)",
    "eta": 5,
    "exact_tail_at_2log_eta": "1249/390625",
    "claimed_upper_bound": "1/625",
    "status": "integral_identity_checked; limiting-measure justification supplied separately"
  },
  "uniform_free_walk": {
    "conditional_outward_probability": "3/4",
    "conditional_inward_probability": "1/4",
    "conditional_drift_away_from_identity": "1/2",
    "qualification": "Finite transition calculation; almost-sure speed requires the separate free-walk argument."
  },
  "qualification": "Does not verify angular counting, generic Zariski density, repaired main theorem, or uniform-in-word-length cone proof."
}