{
 "schema_version": "0.1",
 "name": "local-sat bilayer 6x6x2 G=24 w8 t3 model 0",
 "code_type": "CSS",
 "n": 72,
 "k": 24,
 "checks": {
  "X": [
   [
    2,
    13,
    26,
    36,
    54,
    55,
    59,
    63
   ],
   [
    8,
    26,
    28,
    32,
    34,
    35,
    56,
    63
   ],
   [
    2,
    18,
    33,
    37,
    38,
    46,
    48,
    56
   ],
   [
    3,
    16,
    23,
    25,
    26,
    64
   ],
   [
    28,
    30,
    47,
    48,
    51,
    52,
    62
   ],
   [
    0,
    14,
    17,
    24,
    28,
    33,
    57
   ],
   [
    1,
    3,
    6,
    40,
    52,
    53,
    60,
    61
   ],
   [
    4,
    24,
    25,
    29,
    64,
    69,
    71
   ],
   [
    10,
    19,
    20,
    22,
    31,
    34,
    56,
    58
   ],
   [
    7,
    9,
    10,
    11,
    22,
    39,
    42,
    70
   ],
   [
    11,
    22,
    43,
    44,
    50,
    56,
    57,
    66
   ],
   [
    4,
    6,
    15,
    17,
    20,
    40,
    44,
    45
   ],
   [
    3,
    5,
    15,
    21,
    25,
    29,
    49,
    65
   ],
   [
    9,
    19,
    23,
    32,
    33,
    34,
    42,
    47
   ],
   [
    12,
    14,
    24,
    25,
    37,
    60,
    66,
    69
   ],
   [
    22,
    27,
    35,
    44,
    51,
    53,
    55,
    59
   ],
   [
    1,
    6,
    7,
    13,
    15,
    46,
    48,
    54
   ],
   [
    30,
    36,
    39,
    42,
    44,
    46
   ],
   [
    5,
    35,
    37,
    46,
    50,
    56,
    66,
    67
   ],
   [
    10,
    11,
    21,
    22,
    34,
    40,
    44,
    51
   ],
   [
    10,
    14,
    20,
    29,
    41,
    43,
    66,
    70
   ],
   [
    14,
    15,
    17,
    21,
    24,
    26,
    27,
    71
   ],
   [
    18,
    25,
    50,
    54,
    55,
    58,
    61,
    65
   ],
   [
    7,
    35,
    45,
    49,
    62,
    68,
    69,
    71
   ]
  ],
  "Z": [
   [
    10,
    28,
    30,
    33,
    34,
    38,
    39,
    41
   ],
   [
    2,
    6,
    14,
    17,
    18,
    41,
    54,
    60
   ],
   [
    19,
    30,
    31,
    39,
    41,
    47,
    70
   ],
   [
    5,
    11,
    21,
    66,
    69,
    70,
    71
   ],
   [
    32,
    33,
    55,
    56,
    57,
    58,
    59,
    67
   ],
   [
    18,
    25,
    26,
    37,
    49,
    63,
    67,
    71
   ],
   [
    44,
    45,
    46,
    48,
    49,
    50,
    51,
    65
   ],
   [
    0,
    1,
    6,
    11,
    17,
    22,
    27,
    31
   ],
   [
    0,
    2,
    4,
    5,
    13,
    15,
    24,
    37
   ],
   [
    9,
    40,
    41,
    42,
    43,
    44,
    53
   ],
   [
    13,
    15,
    16,
    25,
    27,
    45,
    55,
    69
   ],
   [
    5,
    14,
    29,
    41,
    57,
    66,
    68,
    71
   ],
   [
    0,
    1,
    32,
    33,
    38,
    54,
    61,
    63
   ],
   [
    4,
    6,
    7,
    9,
    12,
    47,
    52,
    69
   ],
   [
    35,
    36,
    40,
    44,
    50,
    61,
    63,
    68
   ],
   [
    3,
    25,
    49,
    55,
    59,
    61,
    65,
    69
   ],
   [
    2,
    32,
    34,
    35,
    36,
    44,
    45,
    56
   ],
   [
    10,
    51,
    52,
    53,
    55,
    58,
    59,
    70
   ],
   [
    8,
    16,
    19,
    23,
    31,
    32,
    39,
    42
   ],
   [
    13,
    30,
    36,
    37,
    43,
    48,
    66
   ],
   [
    30,
    36,
    49,
    53,
    59,
    61,
    62,
    65
   ],
   [
    22,
    23,
    34,
    35,
    64,
    66,
    69,
    70
   ],
   [
    17,
    19,
    20,
    23,
    24,
    25,
    41,
    65
   ],
   [
    12,
    13,
    54,
    60,
    61
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    29,
    33,
    38,
    57
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    8,
    32,
    39,
    42
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "SAT search (research/local_sat.py build_local_cnf with the grid site list repeated 2 times, n_side=6, G=24, max_weight=8, t=3 detection, anchor radius 3.5, shared_t3 encoding, CaDiCaL 1.9.5 via python-sat) over bilayer 2D-local CSS codes: 2 qubits per site of a 6x6 grid (layers=2), each check anchored at a grid site and acting within radius 3.5 of it, so the interaction radius is at most 7.0 by construction. Model index 0 of the enumeration; distance is a witness-backed upper bound.",
  "references": [],
  "date": "2026-09-28",
  "notes": "Phase 2 (bilayer) of the 2D-local SAT t=2+ campaign (issue #2024); instance b6_G24_w8_t3. Distance is an upper bound from the kit's RIS witness search at 20000 trials per side.",
  "model": "Claude Fable 5.1 (Claude Code)"
 },
 "family": "local-sat-css",
 "locality": {
  "coordinates": [
   [
    0.0,
    0.0
   ],
   [
    0.0,
    0.0
   ],
   [
    1.0,
    0.0
   ],
   [
    1.0,
    0.0
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    0.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    0.0
   ],
   [
    4.0,
    0.0
   ],
   [
    4.0,
    0.0
   ],
   [
    5.0,
    0.0
   ],
   [
    5.0,
    0.0
   ],
   [
    0.0,
    1.0
   ],
   [
    0.0,
    1.0
   ],
   [
    1.0,
    1.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    1.0
   ],
   [
    4.0,
    1.0
   ],
   [
    4.0,
    1.0
   ],
   [
    5.0,
    1.0
   ],
   [
    5.0,
    1.0
   ],
   [
    0.0,
    2.0
   ],
   [
    0.0,
    2.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    2.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    2.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    2.0
   ],
   [
    4.0,
    2.0
   ],
   [
    4.0,
    2.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    0.0,
    3.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    3.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    3.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    3.0
   ],
   [
    4.0,
    3.0
   ],
   [
    4.0,
    3.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    3.0
   ],
   [
    0.0,
    4.0
   ],
   [
    0.0,
    4.0
   ],
   [
    1.0,
    4.0
   ],
   [
    1.0,
    4.0
   ],
   [
    2.0,
    4.0
   ],
   [
    2.0,
    4.0
   ],
   [
    3.0,
    4.0
   ],
   [
    3.0,
    4.0
   ],
   [
    4.0,
    4.0
   ],
   [
    4.0,
    4.0
   ],
   [
    5.0,
    4.0
   ],
   [
    5.0,
    4.0
   ],
   [
    0.0,
    5.0
   ],
   [
    0.0,
    5.0
   ],
   [
    1.0,
    5.0
   ],
   [
    1.0,
    5.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    5.0
   ],
   [
    3.0,
    5.0
   ],
   [
    3.0,
    5.0
   ],
   [
    4.0,
    5.0
   ],
   [
    4.0,
    5.0
   ],
   [
    5.0,
    5.0
   ],
   [
    5.0,
    5.0
   ]
  ],
  "interaction_radius": 5.830951894845301,
  "layers": 2
 }
}