{
  "schema": "proofdama-three-row-boundary-quotient-v1",
  "status": "one_and_two_ply_relations_falsified_variable_weak_closure_next",
  "family": "2n x 3 x 1",
  "projections": {
    "full": "two adjacent cells, border flags, player, FID count and global capture-priority profile",
    "without_fid": "full signature with the 0..80 FID counter factored into a separate product component",
    "local_plus_turn": "two adjacent cells, border flags and player only",
    "local_only": "two adjacent cells and border flags only"
  },
  "benchmarks": [
    {
      "id": "2x3x1",
      "full": 2,
      "without_fid": 2,
      "local_plus_turn": 2,
      "local_only": 2,
      "capture_profiles": 1,
      "alphabet_sha256": "b490151266919c7e788262d150985306b7cc9c98834f6f43cf45ae4d72a22ea9"
    },
    {
      "id": "4x3x1",
      "full": 2573,
      "without_fid": 171,
      "local_plus_turn": 163,
      "local_only": 144,
      "capture_profiles": 4,
      "alphabet_sha256": "60ef715b57f91adb12ec0baeedc17b327973765663ea13c7130f04f95389d785"
    },
    {
      "id": "6x3x1",
      "full": 278203,
      "without_fid": 6018,
      "local_plus_turn": 4511,
      "local_only": 2777,
      "capture_profiles": 8,
      "alphabet_sha256": "e4c85f8589722aea92f453d7fece14bac6f4676c47c0ffa5cbb7915a8e1aac4d"
    },
    {
      "id": "8x3x1",
      "full": 2738799,
      "without_fid": 51385,
      "local_plus_turn": 19302,
      "local_only": 10694,
      "capture_profiles": 16,
      "alphabet_sha256": "6a47287361f2e6feea641901619a6a80045c42e59c3bf2e84e2bffc08a4ba260"
    }
  ],
  "closure_audits": {
    "small_benchmark": "6x3x1",
    "large_benchmark": "8x3x1",
    "fixed_neutral_extension": {
      "embedded_states_found": 106513,
      "outcome_mismatches": 14449,
      "closed": false,
      "artifact": "proofdama-6-to-8-extension-audit.v1.json"
    },
    "movable_neutral_gap": {
      "candidate_pairs": 576165,
      "strong_survivors": 7837,
      "white_root_survives": false,
      "black_root_survives": false,
      "artifact": "proofdama-6-to-8-gap-bisimulation.v1.json"
    },
    "delete_arbitrary_cell": {
      "projections_examined": 164922712,
      "candidate_pairs": 30694340,
      "strong_survivors": 1523793,
      "white_non_losing_survivors": 3466498,
      "black_non_losing_survivors": 3282134,
      "white_root_survives": false,
      "black_root_survives": false,
      "surviving_outcome_contradictions": 0,
      "two_ply_white_non_losing_survivors": 4084852,
      "two_ply_black_non_losing_survivors": 3795042,
      "two_ply_white_root_survives": false,
      "two_ply_black_root_survives": false,
      "two_ply_surviving_outcome_contradictions": 0,
      "artifact": "proofdama-6-to-8-cell-automaton.v1.json"
    }
  },
  "interpretation": "The vacancy encoder is exhaustively equivalent on all certified three-row states. The three tested one-ply extension relations and the fixed two-ply move/response relation are falsified at the certified 6x3x1/8x3x1 roots, so no minimal root automaton is claimed. The next candidate is a variable-length weak closure over explicit local frontier states. A theorem still requires a root-containing fixed point, exact transition-labelled minimisation, closure of every interface obligation, and a held-out 10x3 falsification test."
}