{
  "scope": "Finite evaluation-orbit construction and exhaustive checks of every reachable table entry in the listed examples; independent raw-word evaluation through the stated lengths. No proof assistant, infinite word enumeration, nested-trace or scaffold generator is claimed.",
  "parity_before_refinement": {
    "group_order": 2,
    "evaluation_orbit_size": 1,
    "reachable_summary_states": 2,
    "all_push_inverse_entries_checked": 4,
    "all_boundary_entries_checked": 0,
    "transform_names": [],
    "raw_word_max_length": 6,
    "raw_words_checked": 127
  },
  "parity_swap": {
    "group_order": 2,
    "evaluation_orbit_size": 2,
    "reachable_summary_states": 4,
    "all_push_inverse_entries_checked": 8,
    "all_boundary_entries_checked": 4,
    "transform_names": [
      "swap"
    ],
    "raw_word_max_length": 9,
    "raw_words_checked": 1023
  },
  "parity_multiple_transforms": {
    "group_order": 2,
    "evaluation_orbit_size": 4,
    "reachable_summary_states": 4,
    "all_push_inverse_entries_checked": 8,
    "all_boundary_entries_checked": 16,
    "transform_names": [
      "swap",
      "fibonacci",
      "erase_b",
      "surround"
    ],
    "raw_word_max_length": 9,
    "raw_words_checked": 1023
  },
  "noncommutative_S3": {
    "group_order": 6,
    "evaluation_orbit_size": 36,
    "reachable_summary_states": 972,
    "all_push_inverse_entries_checked": 1944,
    "all_boundary_entries_checked": 3888,
    "transform_names": [
      "swap",
      "fibonacci",
      "erase_b",
      "surround"
    ],
    "raw_word_max_length": 7,
    "raw_words_checked": 255
  },
  "four_observation_pairs_force_four_states": true,
  "last_b_minimal_machine_rejected": true,
  "decimation_horizons": {
    "horizon": 3,
    "state_bound": 128,
    "all_append_inverse_entries": 256,
    "raw_word_max_length": 9,
    "raw_words": 1023,
    "separating_family_max_j": 9,
    "separating_family_observations": [
      [
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      [
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      [
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      [
        1,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      [
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      [
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        0
      ],
      [
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        0,
        0
      ],
      [
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        0
      ],
      [
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0
      ],
      [
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0
      ]
    ],
    "scope": "Finite corroboration only; no all-state-size impossibility proof."
  },
  "general_proof": "Written finite-orbit and permutation argument in companion note."
}