{
 "schema_version": "0.3",
 "name": "[[128,42,6]] weight-12 CSS parity amplification",
 "code_type": "CSS",
 "n": 128,
 "k": 42,
 "checks": {
  "X": [
   [
    0,
    15,
    30,
    45,
    60,
    75,
    90,
    105,
    124
   ],
   [
    1,
    16,
    31,
    46,
    61,
    76,
    91,
    106,
    125
   ],
   [
    2,
    17,
    32,
    47,
    62,
    77,
    92,
    107,
    124,
    125
   ],
   [
    3,
    18,
    33,
    48,
    63,
    78,
    93,
    108,
    126
   ],
   [
    4,
    19,
    34,
    49,
    64,
    79,
    94,
    109,
    124,
    126
   ],
   [
    5,
    20,
    35,
    50,
    65,
    80,
    95,
    110,
    125,
    126
   ],
   [
    6,
    21,
    36,
    51,
    66,
    81,
    96,
    111,
    124,
    125,
    126
   ],
   [
    7,
    22,
    37,
    52,
    67,
    82,
    97,
    112,
    127
   ],
   [
    8,
    23,
    38,
    53,
    68,
    83,
    98,
    113,
    124,
    127
   ],
   [
    9,
    24,
    39,
    54,
    69,
    84,
    99,
    114,
    125,
    127
   ],
   [
    10,
    25,
    40,
    55,
    70,
    85,
    100,
    115,
    124,
    125,
    127
   ],
   [
    11,
    26,
    41,
    56,
    71,
    86,
    101,
    116,
    126,
    127
   ],
   [
    12,
    27,
    42,
    57,
    72,
    87,
    102,
    117,
    124,
    126,
    127
   ],
   [
    13,
    28,
    43,
    58,
    73,
    88,
    103,
    118,
    125,
    126,
    127
   ],
   [
    14,
    29,
    44,
    59,
    74,
    89,
    104,
    119,
    124,
    125,
    126,
    127
   ],
   [
    0,
    2,
    4,
    6,
    8,
    10,
    12,
    14,
    120
   ],
   [
    1,
    2,
    5,
    6,
    9,
    10,
    13,
    14,
    121
   ],
   [
    3,
    4,
    5,
    6,
    11,
    12,
    13,
    14,
    122
   ],
   [
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    123
   ],
   [
    15,
    17,
    19,
    21,
    23,
    25,
    27,
    29,
    120
   ],
   [
    16,
    17,
    20,
    21,
    24,
    25,
    28,
    29,
    121
   ],
   [
    18,
    19,
    20,
    21,
    26,
    27,
    28,
    29,
    122
   ],
   [
    22,
    23,
    24,
    25,
    26,
    27,
    28,
    29,
    123
   ],
   [
    30,
    32,
    34,
    36,
    38,
    40,
    42,
    44,
    120
   ],
   [
    31,
    32,
    35,
    36,
    39,
    40,
    43,
    44,
    121
   ],
   [
    33,
    34,
    35,
    36,
    41,
    42,
    43,
    44,
    122
   ],
   [
    37,
    38,
    39,
    40,
    41,
    42,
    43,
    44,
    123
   ],
   [
    45,
    47,
    49,
    51,
    53,
    55,
    57,
    59,
    120
   ],
   [
    46,
    47,
    50,
    51,
    54,
    55,
    58,
    59,
    121
   ],
   [
    48,
    49,
    50,
    51,
    56,
    57,
    58,
    59,
    122
   ],
   [
    52,
    53,
    54,
    55,
    56,
    57,
    58,
    59,
    123
   ],
   [
    60,
    62,
    64,
    66,
    68,
    70,
    72,
    74,
    120
   ],
   [
    61,
    62,
    65,
    66,
    69,
    70,
    73,
    74,
    121
   ],
   [
    63,
    64,
    65,
    66,
    71,
    72,
    73,
    74,
    122
   ],
   [
    67,
    68,
    69,
    70,
    71,
    72,
    73,
    74,
    123
   ],
   [
    75,
    77,
    79,
    81,
    83,
    85,
    87,
    89,
    120
   ],
   [
    76,
    77,
    80,
    81,
    84,
    85,
    88,
    89,
    121
   ],
   [
    78,
    79,
    80,
    81,
    86,
    87,
    88,
    89,
    122
   ],
   [
    82,
    83,
    84,
    85,
    86,
    87,
    88,
    89,
    123
   ],
   [
    90,
    92,
    94,
    96,
    98,
    100,
    102,
    104,
    120
   ],
   [
    91,
    92,
    95,
    96,
    99,
    100,
    103,
    104,
    121
   ],
   [
    93,
    94,
    95,
    96,
    101,
    102,
    103,
    104,
    122
   ],
   [
    97,
    98,
    99,
    100,
    101,
    102,
    103,
    104,
    123
   ],
   [
    105,
    107,
    109,
    111,
    113,
    115,
    117,
    119,
    120
   ],
   [
    106,
    107,
    110,
    111,
    114,
    115,
    118,
    119,
    121
   ],
   [
    108,
    109,
    110,
    111,
    116,
    117,
    118,
    119,
    122
   ],
   [
    112,
    113,
    114,
    115,
    116,
    117,
    118,
    119,
    123
   ]
  ],
  "Z": [
   [
    0,
    15,
    30,
    45,
    60,
    75,
    90,
    105,
    120
   ],
   [
    1,
    16,
    31,
    46,
    61,
    76,
    91,
    106,
    121
   ],
   [
    2,
    17,
    32,
    47,
    62,
    77,
    92,
    107,
    120,
    121
   ],
   [
    3,
    18,
    33,
    48,
    63,
    78,
    93,
    108,
    122
   ],
   [
    4,
    19,
    34,
    49,
    64,
    79,
    94,
    109,
    120,
    122
   ],
   [
    5,
    20,
    35,
    50,
    65,
    80,
    95,
    110,
    121,
    122
   ],
   [
    6,
    21,
    36,
    51,
    66,
    81,
    96,
    111,
    120,
    121,
    122
   ],
   [
    7,
    22,
    37,
    52,
    67,
    82,
    97,
    112,
    123
   ],
   [
    8,
    23,
    38,
    53,
    68,
    83,
    98,
    113,
    120,
    123
   ],
   [
    9,
    24,
    39,
    54,
    69,
    84,
    99,
    114,
    121,
    123
   ],
   [
    10,
    25,
    40,
    55,
    70,
    85,
    100,
    115,
    120,
    121,
    123
   ],
   [
    11,
    26,
    41,
    56,
    71,
    86,
    101,
    116,
    122,
    123
   ],
   [
    12,
    27,
    42,
    57,
    72,
    87,
    102,
    117,
    120,
    122,
    123
   ],
   [
    13,
    28,
    43,
    58,
    73,
    88,
    103,
    118,
    121,
    122,
    123
   ],
   [
    14,
    29,
    44,
    59,
    74,
    89,
    104,
    119,
    120,
    121,
    122,
    123
   ],
   [
    0,
    2,
    4,
    6,
    8,
    10,
    12,
    14,
    124
   ],
   [
    1,
    2,
    5,
    6,
    9,
    10,
    13,
    14,
    125
   ],
   [
    3,
    4,
    5,
    6,
    11,
    12,
    13,
    14,
    126
   ],
   [
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    127
   ],
   [
    15,
    17,
    19,
    21,
    23,
    25,
    27,
    29,
    124
   ],
   [
    16,
    17,
    20,
    21,
    24,
    25,
    28,
    29,
    125
   ],
   [
    18,
    19,
    20,
    21,
    26,
    27,
    28,
    29,
    126
   ],
   [
    22,
    23,
    24,
    25,
    26,
    27,
    28,
    29,
    127
   ],
   [
    30,
    32,
    34,
    36,
    38,
    40,
    42,
    44,
    124
   ],
   [
    31,
    32,
    35,
    36,
    39,
    40,
    43,
    44,
    125
   ],
   [
    33,
    34,
    35,
    36,
    41,
    42,
    43,
    44,
    126
   ],
   [
    37,
    38,
    39,
    40,
    41,
    42,
    43,
    44,
    127
   ],
   [
    45,
    47,
    49,
    51,
    53,
    55,
    57,
    59,
    124
   ],
   [
    46,
    47,
    50,
    51,
    54,
    55,
    58,
    59,
    125
   ],
   [
    48,
    49,
    50,
    51,
    56,
    57,
    58,
    59,
    126
   ],
   [
    52,
    53,
    54,
    55,
    56,
    57,
    58,
    59,
    127
   ],
   [
    60,
    62,
    64,
    66,
    68,
    70,
    72,
    74,
    124
   ],
   [
    61,
    62,
    65,
    66,
    69,
    70,
    73,
    74,
    125
   ],
   [
    63,
    64,
    65,
    66,
    71,
    72,
    73,
    74,
    126
   ],
   [
    67,
    68,
    69,
    70,
    71,
    72,
    73,
    74,
    127
   ],
   [
    75,
    77,
    79,
    81,
    83,
    85,
    87,
    89,
    124
   ],
   [
    76,
    77,
    80,
    81,
    84,
    85,
    88,
    89,
    125
   ],
   [
    78,
    79,
    80,
    81,
    86,
    87,
    88,
    89,
    126
   ],
   [
    82,
    83,
    84,
    85,
    86,
    87,
    88,
    89,
    127
   ],
   [
    90,
    92,
    94,
    96,
    98,
    100,
    102,
    104,
    124
   ],
   [
    91,
    92,
    95,
    96,
    99,
    100,
    103,
    104,
    125
   ],
   [
    93,
    94,
    95,
    96,
    101,
    102,
    103,
    104,
    126
   ],
   [
    97,
    98,
    99,
    100,
    101,
    102,
    103,
    104,
    127
   ],
   [
    105,
    107,
    109,
    111,
    113,
    115,
    117,
    119,
    124
   ],
   [
    106,
    107,
    110,
    111,
    114,
    115,
    118,
    119,
    125
   ],
   [
    108,
    109,
    110,
    111,
    116,
    117,
    118,
    119,
    126
   ],
   [
    112,
    113,
    114,
    115,
    116,
    117,
    118,
    119,
    127
   ]
  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    62,
    71,
    74,
    92,
    101,
    104
   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    81,
    83,
    88,
    96,
    98,
    103
   ]
  }
 },
 "provenance": {
  "authors": [
   "@nihoniumqc"
  ],
  "construction": "Central CSS tensor product of board inputs 8-6-2 and 15-7-3, in that order, using arXiv:2609.37231 Eqs. (14)-(15). Retained zero-based X/Z row indices: [[0], [0], [0, 1, 2, 3], [0, 1, 2, 3]]. Input attribution: 8-6-2: @MathysRennela; 15-7-3: @FarLab. The research note gives the complete reproducible matrix recipe.",
  "references": [
   "https://arxiv.org/abs/2609.37231",
   "https://arxiv.org/abs/1512.07081",
   "https://arxiv.org/abs/2306.16400"
  ],
  "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": 0.0027636754974999967,
   "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": [
   [
    6.0,
    7.0
   ],
   [
    0.0,
    7.0
   ],
   [
    3.0,
    7.0
   ],
   [
    2.0,
    2.0
   ],
   [
    5.0,
    5.0
   ],
   [
    0.0,
    5.0
   ],
   [
    2.0,
    7.0
   ],
   [
    5.0,
    7.0
   ],
   [
    5.0,
    6.0
   ],
   [
    2.0,
    4.0
   ],
   [
    1.0,
    7.0
   ],
   [
    5.0,
    5.0
   ],
   [
    3.0,
    5.0
   ],
   [
    1.0,
    6.0
   ],
   [
    2.0,
    6.0
   ],
   [
    7.0,
    5.0
   ],
   [
    1.0,
    3.0
   ],
   [
    5.0,
    4.0
   ],
   [
    6.0,
    0.0
   ],
   [
    7.0,
    2.0
   ],
   [
    3.0,
    1.0
   ],
   [
    6.0,
    4.0
   ],
   [
    6.0,
    2.0
   ],
   [
    7.0,
    2.0
   ],
   [
    4.0,
    0.0
   ],
   [
    6.0,
    4.0
   ],
   [
    6.0,
    0.0
   ],
   [
    6.0,
    1.0
   ],
   [
    5.0,
    3.0
   ],
   [
    6.0,
    2.0
   ],
   [
    3.0,
    5.0
   ],
   [
    0.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    1.0,
    0.0
   ],
   [
    4.0,
    0.0
   ],
   [
    0.0,
    0.0
   ],
   [
    2.0,
    3.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    1.0
   ],
   [
    0.0,
    0.0
   ],
   [
    0.0,
    3.0
   ],
   [
    4.0,
    1.0
   ],
   [
    3.0,
    1.0
   ],
   [
    0.0,
    1.0
   ],
   [
    0.0,
    1.0
   ],
   [
    5.0,
    7.0
   ],
   [
    0.0,
    7.0
   ],
   [
    1.0,
    6.0
   ],
   [
    2.0,
    3.0
   ],
   [
    4.0,
    3.0
   ],
   [
    0.0,
    5.0
   ],
   [
    2.0,
    7.0
   ],
   [
    2.0,
    5.0
   ],
   [
    4.0,
    5.0
   ],
   [
    0.0,
    4.0
   ],
   [
    1.0,
    7.0
   ],
   [
    4.0,
    5.0
   ],
   [
    2.0,
    4.0
   ],
   [
    0.0,
    4.0
   ],
   [
    1.0,
    5.0
   ],
   [
    7.0,
    3.0
   ],
   [
    1.0,
    2.0
   ],
   [
    4.0,
    2.0
   ],
   [
    7.0,
    0.0
   ],
   [
    7.0,
    0.0
   ],
   [
    2.0,
    0.0
   ],
   [
    5.0,
    3.0
   ],
   [
    7.0,
    3.0
   ],
   [
    7.0,
    1.0
   ],
   [
    3.0,
    0.0
   ],
   [
    4.0,
    2.0
   ],
   [
    7.0,
    1.0
   ],
   [
    6.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    0.0
   ],
   [
    7.0,
    7.0
   ],
   [
    0.0,
    6.0
   ],
   [
    3.0,
    7.0
   ],
   [
    5.0,
    4.0
   ],
   [
    6.0,
    5.0
   ],
   [
    1.0,
    5.0
   ],
   [
    4.0,
    6.0
   ],
   [
    6.0,
    7.0
   ],
   [
    6.0,
    6.0
   ],
   [
    2.0,
    5.0
   ],
   [
    4.0,
    7.0
   ],
   [
    6.0,
    6.0
   ],
   [
    6.0,
    5.0
   ],
   [
    2.0,
    6.0
   ],
   [
    3.0,
    6.0
   ],
   [
    7.0,
    7.0
   ],
   [
    0.0,
    6.0
   ],
   [
    4.0,
    6.0
   ],
   [
    6.0,
    3.0
   ],
   [
    7.0,
    4.0
   ],
   [
    3.0,
    2.0
   ],
   [
    5.0,
    6.0
   ],
   [
    7.0,
    6.0
   ],
   [
    7.0,
    6.0
   ],
   [
    4.0,
    3.0
   ],
   [
    4.0,
    7.0
   ],
   [
    7.0,
    5.0
   ],
   [
    7.0,
    4.0
   ],
   [
    3.0,
    4.0
   ],
   [
    3.0,
    6.0
   ],
   [
    6.0,
    3.0
   ],
   [
    0.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    0.0
   ],
   [
    5.0,
    0.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    1.0,
    2.0
   ],
   [
    5.0,
    0.0
   ],
   [
    4.0,
    1.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    0.0
   ],
   [
    4.0,
    4.0
   ],
   [
    1.0,
    4.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    4.0
   ],
   [
    4.0,
    4.0
   ],
   [
    1.0,
    4.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    3.0
   ]
  ],
  "layers": 2,
  "interaction_radius": 6.0828,
  "contributed_by": {
   "by": [
    "@dorakingx"
   ],
   "date": "2026-10-07",
   "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."
  }
 }
}
