{
 "schema_version": "0.1",
 "name": "local-sat 5x5 G=8 w8 t3 model 0",
 "code_type": "CSS",
 "n": 25,
 "k": 9,
 "checks": {
  "X": [
   [
    3,
    7,
    8,
    9,
    11,
    12,
    14,
    23
   ],
   [
    4,
    14,
    18,
    19
   ],
   [
    12,
    15,
    16,
    17,
    19,
    21,
    22,
    23
   ],
   [
    1,
    2,
    6,
    9,
    12,
    17
   ],
   [
    1,
    5,
    7,
    10,
    13,
    16,
    17,
    21
   ],
   [
    6,
    10,
    11,
    12,
    15,
    18,
    20,
    21
   ],
   [
    8,
    12,
    13,
    14,
    17,
    18,
    22,
    24
   ],
   [
    0,
    1,
    2,
    5,
    8,
    11,
    12,
    16
   ]
  ],
  "Z": [
   [
    5,
    6,
    10,
    13,
    15,
    16,
    17,
    21
   ],
   [
    7,
    18,
    19,
    21,
    22,
    23
   ],
   [
    2,
    3,
    6,
    7,
    8,
    13,
    14,
    18
   ],
   [
    4,
    8,
    9,
    12,
    14,
    18,
    19
   ],
   [
    11,
    15,
    16,
    20,
    21,
    23
   ],
   [
    12,
    14,
    16,
    17,
    18,
    22,
    24
   ],
   [
    0,
    1,
    5,
    8,
    10,
    12,
    16
   ],
   [
    1,
    2,
    5,
    6,
    9,
    11
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    4,
    7,
    14,
    22
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    1,
    6,
    15,
    16
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "SAT search on a 5x5 grid (research/local_sat.py::enumerate_local_sat_codes(n_side=5, n_generators=8, max_weight=8, t=3, radius=2.0, layers=1, solver='cadical', conf_budget=3000000, max_rounds=40, max_codes=40, seed=0, shared_t3=True)). Weight <= 8 CSS checks, interaction radius 4.0, single layer. The encoder forbids every X and Z Pauli of weight <= 3, so d >= 4; enumerate_local_sat_codes also post-checks each enumerated error vector for a nonzero syndrome before yielding, so the claim does not rest on the encoding alone. Screened against the board's Pareto frontier over (n, k, d, w), and re-verified with verify/validate_candidate.py (passed: true, board_advancing: true, no lighter logical in 3500 RIS trials).",
  "origin": "submission",
  "date": "2026-09-25",
  "model": "MiMo-V2.6-Flash",
  "notes": "Checked against the board: exact_duplicate_of null, wl_equivalent_of null, dominated_by [] in 2D-local single x weight-8, board_advancing true. Checked, not equivalent to any existing entry."
 },
 "family": "other",
 "locality": {
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  "layers": 1
 }
}