{
  "reference_reproductions": [
    {
      "K": 9,
      "decay": "3900",
      "residual": "2523/160",
      "maximum_violation": "0",
      "joint_return_lower": "8046297159/8112104000",
      "scope": "Exact finite-state generator inequality and rational exp bound; no simulation used, Lean not rerun.",
      "numerical_return_min": 0.9921325118964676,
      "numerical_return_max": 0.992132511896469,
      "stationary_return_exact": "1010143506027271073771689652423964440268324000000/1018153819068586595867806661771770404318808648081",
      "stationary_return_float": 0.9921325119139234,
      "partition_ceiling": "65025/65536",
      "transition_row_sum_error": 1.7594259382747168e-11
    },
    {
      "K": 20,
      "decay": "9000",
      "residual": "2535/131072",
      "maximum_violation": "0",
      "joint_return_lower": "7077818258231/7077927321600",
      "scope": "Exact finite-state generator inequality and rational exp bound; no simulation used, Lean not rerun.",
      "numerical_return_min": 0.9999961087928073,
      "numerical_return_max": 0.9999961087928125,
      "stationary_return_exact": "2601964804182791550478200534386562765635934680938867669731276348792464536626138640529811619928563521359272562500/2601974930129662751847434644820874875245315008851205465811738541722151232347441884632710489078093203717704269001",
      "stationary_return_float": 0.9999961083610938,
      "partition_ceiling": "274876858369/274877906944",
      "transition_row_sum_error": 4.317206592219236e-10
    }
  ],
  "operating_box": {
    "decay": "1800",
    "residual": "279/32",
    "maximum_violation": "0",
    "joint_return_lower": "114080769/115203200",
    "scope": "Exact finite-state generator inequality and rational exp bound; no simulation used, Lean not rerun."
  },
  "configured_model": {
    "capacity": 9,
    "forward": "1000",
    "reverse": "1",
    "coupling": "1/10",
    "decay": "3900",
    "residual": "2523/160",
    "maximum_violation": "0",
    "joint_return_lower": "8046297159/8112104000",
    "scope": "Exact finite-state generator inequality and rational exp bound; no simulation used, Lean not rerun."
  },
  "best_17_resident_partition": "32385/32768",
  "sharp_composition_gap": "2/9",
  "measurement_tolerance_strict": "1/9",
  "kernel_row_identity_error": 1.1102230246251565e-16,
  "sample_cycle_completed": true,
  "sample_cycle_success": true,
  "lineage_final_range": [
    0.20603277611155785,
    0.20603277611155812
  ],
  "family_final_range": [
    0.7828167842385624,
    0.7828167842385635
  ],
  "scope": "Finite-chain matrix exponentials and restart recursions are numerical evaluations, not certified probabilities. Exact rational generator checks are separate. The four labels use disjoint supports, not bistability or contamination correction."
}