{
 "schema_version": "0.3",
 "name": "[[132,32,8]] weight-11 CSS parity amplification",
 "code_type": "CSS",
 "n": 132,
 "k": 32,
 "checks": {
  "X": [
   [
    0,
    20,
    40,
    60,
    80,
    100,
    127
   ],
   [
    1,
    21,
    41,
    61,
    81,
    101,
    127,
    130,
    131
   ],
   [
    2,
    22,
    42,
    62,
    82,
    102,
    128,
    130,
    131
   ],
   [
    3,
    23,
    43,
    63,
    83,
    103,
    127,
    131
   ],
   [
    4,
    24,
    44,
    64,
    84,
    104,
    126,
    131
   ],
   [
    5,
    25,
    45,
    65,
    85,
    105,
    128,
    131
   ],
   [
    6,
    26,
    46,
    66,
    86,
    106,
    128,
    129
   ],
   [
    7,
    27,
    47,
    67,
    87,
    107,
    126,
    129,
    131
   ],
   [
    8,
    28,
    48,
    68,
    88,
    108,
    126,
    130
   ],
   [
    9,
    29,
    49,
    69,
    89,
    109,
    127,
    129,
    130,
    131
   ],
   [
    10,
    30,
    50,
    70,
    90,
    110,
    127,
    130
   ],
   [
    11,
    31,
    51,
    71,
    91,
    111,
    128,
    129,
    131
   ],
   [
    12,
    32,
    52,
    72,
    92,
    112,
    128,
    130
   ],
   [
    13,
    33,
    53,
    73,
    93,
    113,
    126,
    127,
    128,
    129,
    131
   ],
   [
    14,
    34,
    54,
    74,
    94,
    114,
    128
   ],
   [
    15,
    35,
    55,
    75,
    95,
    115,
    126,
    129
   ],
   [
    16,
    36,
    56,
    76,
    96,
    116,
    127,
    129,
    130
   ],
   [
    17,
    37,
    57,
    77,
    97,
    117,
    126,
    127,
    128,
    129
   ],
   [
    18,
    38,
    58,
    78,
    98,
    118,
    126
   ],
   [
    19,
    39,
    59,
    79,
    99,
    119,
    126,
    130,
    131
   ],
   [
    4,
    7,
    8,
    13,
    15,
    17,
    18,
    19,
    120
   ],
   [
    0,
    1,
    3,
    9,
    10,
    13,
    16,
    17,
    121
   ],
   [
    2,
    5,
    6,
    11,
    12,
    13,
    14,
    17,
    122
   ],
   [
    6,
    7,
    9,
    11,
    13,
    15,
    16,
    17,
    123
   ],
   [
    1,
    2,
    8,
    9,
    10,
    12,
    16,
    19,
    124
   ],
   [
    1,
    2,
    3,
    4,
    5,
    7,
    9,
    11,
    13,
    19,
    125
   ],
   [
    24,
    27,
    28,
    33,
    35,
    37,
    38,
    39,
    120
   ],
   [
    20,
    21,
    23,
    29,
    30,
    33,
    36,
    37,
    121
   ],
   [
    22,
    25,
    26,
    31,
    32,
    33,
    34,
    37,
    122
   ],
   [
    26,
    27,
    29,
    31,
    33,
    35,
    36,
    37,
    123
   ],
   [
    21,
    22,
    28,
    29,
    30,
    32,
    36,
    39,
    124
   ],
   [
    21,
    22,
    23,
    24,
    25,
    27,
    29,
    31,
    33,
    39,
    125
   ],
   [
    44,
    47,
    48,
    53,
    55,
    57,
    58,
    59,
    120
   ],
   [
    40,
    41,
    43,
    49,
    50,
    53,
    56,
    57,
    121
   ],
   [
    42,
    45,
    46,
    51,
    52,
    53,
    54,
    57,
    122
   ],
   [
    46,
    47,
    49,
    51,
    53,
    55,
    56,
    57,
    123
   ],
   [
    41,
    42,
    48,
    49,
    50,
    52,
    56,
    59,
    124
   ],
   [
    41,
    42,
    43,
    44,
    45,
    47,
    49,
    51,
    53,
    59,
    125
   ],
   [
    64,
    67,
    68,
    73,
    75,
    77,
    78,
    79,
    120
   ],
   [
    60,
    61,
    63,
    69,
    70,
    73,
    76,
    77,
    121
   ],
   [
    62,
    65,
    66,
    71,
    72,
    73,
    74,
    77,
    122
   ],
   [
    66,
    67,
    69,
    71,
    73,
    75,
    76,
    77,
    123
   ],
   [
    61,
    62,
    68,
    69,
    70,
    72,
    76,
    79,
    124
   ],
   [
    61,
    62,
    63,
    64,
    65,
    67,
    69,
    71,
    73,
    79,
    125
   ],
   [
    84,
    87,
    88,
    93,
    95,
    97,
    98,
    99,
    120
   ],
   [
    80,
    81,
    83,
    89,
    90,
    93,
    96,
    97,
    121
   ],
   [
    82,
    85,
    86,
    91,
    92,
    93,
    94,
    97,
    122
   ],
   [
    86,
    87,
    89,
    91,
    93,
    95,
    96,
    97,
    123
   ],
   [
    81,
    82,
    88,
    89,
    90,
    92,
    96,
    99,
    124
   ],
   [
    81,
    82,
    83,
    84,
    85,
    87,
    89,
    91,
    93,
    99,
    125
   ],
   [
    104,
    107,
    108,
    113,
    115,
    117,
    118,
    119,
    120
   ],
   [
    100,
    101,
    103,
    109,
    110,
    113,
    116,
    117,
    121
   ],
   [
    102,
    105,
    106,
    111,
    112,
    113,
    114,
    117,
    122
   ],
   [
    106,
    107,
    109,
    111,
    113,
    115,
    116,
    117,
    123
   ],
   [
    101,
    102,
    108,
    109,
    110,
    112,
    116,
    119,
    124
   ],
   [
    101,
    102,
    103,
    104,
    105,
    107,
    109,
    111,
    113,
    119,
    125
   ]
  ],
  "Z": [
   [
    0,
    20,
    40,
    60,
    80,
    100,
    121
   ],
   [
    1,
    21,
    41,
    61,
    81,
    101,
    121,
    124,
    125
   ],
   [
    2,
    22,
    42,
    62,
    82,
    102,
    122,
    124,
    125
   ],
   [
    3,
    23,
    43,
    63,
    83,
    103,
    121,
    125
   ],
   [
    4,
    24,
    44,
    64,
    84,
    104,
    120,
    125
   ],
   [
    5,
    25,
    45,
    65,
    85,
    105,
    122,
    125
   ],
   [
    6,
    26,
    46,
    66,
    86,
    106,
    122,
    123
   ],
   [
    7,
    27,
    47,
    67,
    87,
    107,
    120,
    123,
    125
   ],
   [
    8,
    28,
    48,
    68,
    88,
    108,
    120,
    124
   ],
   [
    9,
    29,
    49,
    69,
    89,
    109,
    121,
    123,
    124,
    125
   ],
   [
    10,
    30,
    50,
    70,
    90,
    110,
    121,
    124
   ],
   [
    11,
    31,
    51,
    71,
    91,
    111,
    122,
    123,
    125
   ],
   [
    12,
    32,
    52,
    72,
    92,
    112,
    122,
    124
   ],
   [
    13,
    33,
    53,
    73,
    93,
    113,
    120,
    121,
    122,
    123,
    125
   ],
   [
    14,
    34,
    54,
    74,
    94,
    114,
    122
   ],
   [
    15,
    35,
    55,
    75,
    95,
    115,
    120,
    123
   ],
   [
    16,
    36,
    56,
    76,
    96,
    116,
    121,
    123,
    124
   ],
   [
    17,
    37,
    57,
    77,
    97,
    117,
    120,
    121,
    122,
    123
   ],
   [
    18,
    38,
    58,
    78,
    98,
    118,
    120
   ],
   [
    19,
    39,
    59,
    79,
    99,
    119,
    120,
    124,
    125
   ],
   [
    4,
    7,
    8,
    13,
    15,
    17,
    18,
    19,
    126
   ],
   [
    0,
    1,
    3,
    9,
    10,
    13,
    16,
    17,
    127
   ],
   [
    2,
    5,
    6,
    11,
    12,
    13,
    14,
    17,
    128
   ],
   [
    6,
    7,
    9,
    11,
    13,
    15,
    16,
    17,
    129
   ],
   [
    1,
    2,
    8,
    9,
    10,
    12,
    16,
    19,
    130
   ],
   [
    1,
    2,
    3,
    4,
    5,
    7,
    9,
    11,
    13,
    19,
    131
   ],
   [
    24,
    27,
    28,
    33,
    35,
    37,
    38,
    39,
    126
   ],
   [
    20,
    21,
    23,
    29,
    30,
    33,
    36,
    37,
    127
   ],
   [
    22,
    25,
    26,
    31,
    32,
    33,
    34,
    37,
    128
   ],
   [
    26,
    27,
    29,
    31,
    33,
    35,
    36,
    37,
    129
   ],
   [
    21,
    22,
    28,
    29,
    30,
    32,
    36,
    39,
    130
   ],
   [
    21,
    22,
    23,
    24,
    25,
    27,
    29,
    31,
    33,
    39,
    131
   ],
   [
    44,
    47,
    48,
    53,
    55,
    57,
    58,
    59,
    126
   ],
   [
    40,
    41,
    43,
    49,
    50,
    53,
    56,
    57,
    127
   ],
   [
    42,
    45,
    46,
    51,
    52,
    53,
    54,
    57,
    128
   ],
   [
    46,
    47,
    49,
    51,
    53,
    55,
    56,
    57,
    129
   ],
   [
    41,
    42,
    48,
    49,
    50,
    52,
    56,
    59,
    130
   ],
   [
    41,
    42,
    43,
    44,
    45,
    47,
    49,
    51,
    53,
    59,
    131
   ],
   [
    64,
    67,
    68,
    73,
    75,
    77,
    78,
    79,
    126
   ],
   [
    60,
    61,
    63,
    69,
    70,
    73,
    76,
    77,
    127
   ],
   [
    62,
    65,
    66,
    71,
    72,
    73,
    74,
    77,
    128
   ],
   [
    66,
    67,
    69,
    71,
    73,
    75,
    76,
    77,
    129
   ],
   [
    61,
    62,
    68,
    69,
    70,
    72,
    76,
    79,
    130
   ],
   [
    61,
    62,
    63,
    64,
    65,
    67,
    69,
    71,
    73,
    79,
    131
   ],
   [
    84,
    87,
    88,
    93,
    95,
    97,
    98,
    99,
    126
   ],
   [
    80,
    81,
    83,
    89,
    90,
    93,
    96,
    97,
    127
   ],
   [
    82,
    85,
    86,
    91,
    92,
    93,
    94,
    97,
    128
   ],
   [
    86,
    87,
    89,
    91,
    93,
    95,
    96,
    97,
    129
   ],
   [
    81,
    82,
    88,
    89,
    90,
    92,
    96,
    99,
    130
   ],
   [
    81,
    82,
    83,
    84,
    85,
    87,
    89,
    91,
    93,
    99,
    131
   ],
   [
    104,
    107,
    108,
    113,
    115,
    117,
    118,
    119,
    126
   ],
   [
    100,
    101,
    103,
    109,
    110,
    113,
    116,
    117,
    127
   ],
   [
    102,
    105,
    106,
    111,
    112,
    113,
    114,
    117,
    128
   ],
   [
    106,
    107,
    109,
    111,
    113,
    115,
    116,
    117,
    129
   ],
   [
    101,
    102,
    108,
    109,
    110,
    112,
    116,
    119,
    130
   ],
   [
    101,
    102,
    103,
    104,
    105,
    107,
    109,
    111,
    113,
    119,
    131
   ]
  ]
 },
 "distance": {
  "d": 8,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    82,
    90,
    93,
    95,
    102,
    110,
    113,
    115
   ]
  },
  "Z": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    41,
    45,
    49,
    51,
    101,
    105,
    109,
    111
   ]
  }
 },
 "provenance": {
  "authors": [
   "@nihoniumqc"
  ],
  "construction": "Central CSS tensor product of board inputs 6-4-2 and 20-8-4, in that order, using arXiv:2609.37231 Eqs. (14)-(15). Retained zero-based X/Z row indices: [[0], [0], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5]]. Input attribution: 6-4-2: @MathysRennela; 20-8-4: @EthanFeld. The research note gives the complete reproducible matrix recipe.",
  "references": [
   "https://arxiv.org/abs/2609.37231",
   "https://arxiv.org/abs/1512.07081"
  ],
  "date": "2026-10-03",
  "notes": "Known tensor construction; literature novelty unverified. Final duplicate and WL-signature checks use upstream da1f2c0a1611b215376b249c139f4951e2394418. Neither check constitutes exhaustive equivalence testing. X and Z distances remain witnessed upper bounds.",
  "model": "GPT-6",
  "origin": "submission",
  "novelty": "unknown",
  "search_budget": {
   "candidates_screened": 7,
   "tool": "RIS pilot and witness-returning confirmation",
   "wall_clock_hours": 0.0028037335763888885,
   "notes": "The table reports confirmation after the initial 500-trial-per-side pilot. The deepest rung is one million trials per side.",
   "ris_trials_per_side": 1000000
  }
 },
 "family": "other",
 "locality": {
  "coordinates": [
   [
    1.0,
    0.0
   ],
   [
    4.0,
    0.0
   ],
   [
    5.0,
    4.0
   ],
   [
    5.0,
    0.0
   ],
   [
    5.0,
    2.0
   ],
   [
    6.0,
    4.0
   ],
   [
    2.0,
    5.0
   ],
   [
    6.0,
    3.0
   ],
   [
    6.0,
    1.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    0.0
   ],
   [
    6.0,
    4.0
   ],
   [
    2.0,
    3.0
   ],
   [
    3.0,
    1.0
   ],
   [
    1.0,
    5.0
   ],
   [
    5.0,
    5.0
   ],
   [
    4.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    6.0,
    5.0
   ],
   [
    5.0,
    1.0
   ],
   [
    1.0,
    1.0
   ],
   [
    5.0,
    4.0
   ],
   [
    2.0,
    8.0
   ],
   [
    4.0,
    4.0
   ],
   [
    6.0,
    7.0
   ],
   [
    4.0,
    8.0
   ],
   [
    1.0,
    8.0
   ],
   [
    6.0,
    8.0
   ],
   [
    6.0,
    6.0
   ],
   [
    1.0,
    6.0
   ],
   [
    2.0,
    4.0
   ],
   [
    5.0,
    8.0
   ],
   [
    1.0,
    7.0
   ],
   [
    2.0,
    6.0
   ],
   [
    1.0,
    9.0
   ],
   [
    5.0,
    9.0
   ],
   [
    1.0,
    6.0
   ],
   [
    2.0,
    6.0
   ],
   [
    5.0,
    9.0
   ],
   [
    6.0,
    6.0
   ],
   [
    0.0,
    2.0
   ],
   [
    2.0,
    4.0
   ],
   [
    3.0,
    7.0
   ],
   [
    6.0,
    3.0
   ],
   [
    6.0,
    7.0
   ],
   [
    4.0,
    8.0
   ],
   [
    3.0,
    9.0
   ],
   [
    6.0,
    8.0
   ],
   [
    5.0,
    6.0
   ],
   [
    2.0,
    7.0
   ],
   [
    1.0,
    3.0
   ],
   [
    5.0,
    8.0
   ],
   [
    1.0,
    8.0
   ],
   [
    4.0,
    6.0
   ],
   [
    2.0,
    8.0
   ],
   [
    4.0,
    9.0
   ],
   [
    3.0,
    6.0
   ],
   [
    2.0,
    7.0
   ],
   [
    4.0,
    9.0
   ],
   [
    4.0,
    6.0
   ],
   [
    0.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    1.0,
    7.0
   ],
   [
    2.0,
    2.0
   ],
   [
    5.0,
    7.0
   ],
   [
    5.0,
    7.0
   ],
   [
    2.0,
    9.0
   ],
   [
    4.0,
    7.0
   ],
   [
    4.0,
    5.0
   ],
   [
    0.0,
    6.0
   ],
   [
    0.0,
    2.0
   ],
   [
    4.0,
    7.0
   ],
   [
    0.0,
    7.0
   ],
   [
    0.0,
    5.0
   ],
   [
    1.0,
    9.0
   ],
   [
    2.0,
    9.0
   ],
   [
    1.0,
    5.0
   ],
   [
    0.0,
    5.0
   ],
   [
    3.0,
    8.0
   ],
   [
    2.0,
    5.0
   ],
   [
    1.0,
    0.0
   ],
   [
    3.0,
    0.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    0.0
   ],
   [
    6.0,
    2.0
   ],
   [
    5.0,
    3.0
   ],
   [
    3.0,
    5.0
   ],
   [
    6.0,
    2.0
   ],
   [
    6.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    4.0,
    0.0
   ],
   [
    5.0,
    2.0
   ],
   [
    4.0,
    4.0
   ],
   [
    4.0,
    1.0
   ],
   [
    0.0,
    4.0
   ],
   [
    3.0,
    4.0
   ],
   [
    2.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    6.0,
    5.0
   ],
   [
    5.0,
    1.0
   ],
   [
    0.0,
    0.0
   ],
   [
    2.0,
    0.0
   ],
   [
    0.0,
    3.0
   ],
   [
    2.0,
    0.0
   ],
   [
    3.0,
    3.0
   ],
   [
    1.0,
    4.0
   ],
   [
    0.0,
    6.0
   ],
   [
    4.0,
    3.0
   ],
   [
    3.0,
    2.0
   ],
   [
    1.0,
    1.0
   ],
   [
    0.0,
    0.0
   ],
   [
    1.0,
    4.0
   ],
   [
    0.0,
    3.0
   ],
   [
    0.0,
    4.0
   ],
   [
    0.0,
    8.0
   ],
   [
    0.0,
    7.0
   ],
   [
    0.0,
    1.0
   ],
   [
    1.0,
    3.0
   ],
   [
    3.0,
    8.0
   ],
   [
    3.0,
    2.0
   ],
   [
    5.0,
    6.0
   ],
   [
    1.0,
    2.0
   ],
   [
    3.0,
    6.0
   ],
   [
    3.0,
    5.0
   ],
   [
    2.0,
    3.0
   ],
   [
    4.0,
    3.0
   ],
   [
    5.0,
    5.0
   ],
   [
    1.0,
    2.0
   ],
   [
    3.0,
    7.0
   ],
   [
    4.0,
    5.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    4.0
   ]
  ],
  "layers": 2,
  "interaction_radius": 6.0828,
  "contributed_by": {
   "by": [
    "@dorakingx"
   ],
   "date": "2026-10-04",
   "method": "Simulated annealing over site assignments on an integer grid with the repo's own research/local2d/fold_layout.search_layout (max-diameter objective, several bounding boxes and seeds); single layer at radius 4 tried first, then two layers at 7. Radius and per-site occupancy re-measured with the verifier's rule."
  }
 }
}