{
 "schema_version": "0.2",
 "name": "[[190,78,3]] reduction of [[201,78,3]]",
 "code_type": "CSS",
 "n": 190,
 "k": 78,
 "checks": {
  "X": [
   [
    0,
    12,
    24,
    36,
    48,
    60,
    72,
    84,
    96,
    108,
    120,
    132,
    144,
    156,
    168,
    180
   ],
   [
    1,
    13,
    25,
    37,
    49,
    61,
    73,
    85,
    97,
    109,
    121,
    133,
    145,
    157,
    169,
    181
   ],
   [
    2,
    14,
    26,
    38,
    50,
    62,
    74,
    86,
    98,
    110,
    122,
    134,
    146,
    158,
    170,
    182,
    186
   ],
   [
    3,
    15,
    27,
    39,
    51,
    63,
    75,
    87,
    99,
    111,
    123,
    135,
    147,
    159,
    171,
    183,
    186
   ],
   [
    4,
    16,
    28,
    40,
    52,
    64,
    76,
    88,
    100,
    112,
    124,
    136,
    148,
    160,
    172,
    184,
    186
   ],
   [
    5,
    17,
    29,
    41,
    53,
    65,
    77,
    89,
    101,
    113,
    125,
    137,
    149,
    161,
    173,
    185,
    186
   ],
   [
    6,
    12,
    30,
    36,
    54,
    60,
    78,
    84,
    102,
    108,
    126,
    132,
    150,
    156,
    174,
    180,
    187
   ],
   [
    7,
    13,
    31,
    37,
    55,
    61,
    79,
    85,
    103,
    109,
    127,
    133,
    151,
    157,
    175,
    181,
    187
   ],
   [
    8,
    14,
    32,
    38,
    56,
    62,
    80,
    86,
    104,
    110,
    128,
    134,
    152,
    158,
    176,
    182
   ],
   [
    9,
    15,
    33,
    39,
    57,
    63,
    81,
    87,
    105,
    111,
    129,
    135,
    153,
    159,
    177,
    183
   ],
   [
    10,
    16,
    34,
    40,
    58,
    64,
    82,
    88,
    106,
    112,
    130,
    136,
    154,
    160,
    178,
    184,
    187
   ],
   [
    11,
    17,
    35,
    41,
    59,
    65,
    83,
    89,
    107,
    113,
    131,
    137,
    155,
    161,
    179,
    185,
    187
   ],
   [
    18,
    24,
    30,
    36,
    66,
    72,
    78,
    84,
    114,
    120,
    126,
    132,
    162,
    168,
    174,
    180,
    188
   ],
   [
    19,
    25,
    31,
    37,
    67,
    73,
    79,
    85,
    115,
    121,
    127,
    133,
    163,
    169,
    175,
    181,
    188
   ],
   [
    20,
    26,
    32,
    38,
    68,
    74,
    80,
    86,
    116,
    122,
    128,
    134,
    164,
    170,
    176,
    182
   ],
   [
    21,
    27,
    33,
    39,
    69,
    75,
    81,
    87,
    117,
    123,
    129,
    135,
    165,
    171,
    177,
    183
   ],
   [
    22,
    28,
    34,
    40,
    70,
    76,
    82,
    88,
    118,
    124,
    130,
    136,
    166,
    172,
    178,
    184,
    188
   ],
   [
    23,
    29,
    35,
    41,
    71,
    77,
    83,
    89,
    119,
    125,
    131,
    137,
    167,
    173,
    179,
    185,
    188
   ],
   [
    42,
    48,
    54,
    60,
    66,
    72,
    78,
    84,
    138,
    144,
    150,
    156,
    162,
    168,
    174,
    180
   ],
   [
    43,
    49,
    55,
    61,
    67,
    73,
    79,
    85,
    139,
    145,
    151,
    157,
    163,
    169,
    175,
    181
   ],
   [
    44,
    50,
    56,
    62,
    68,
    74,
    80,
    86,
    140,
    146,
    152,
    158,
    164,
    170,
    176,
    182,
    189
   ],
   [
    45,
    51,
    57,
    63,
    69,
    75,
    81,
    87,
    141,
    147,
    153,
    159,
    165,
    171,
    177,
    183,
    189
   ],
   [
    46,
    52,
    58,
    64,
    70,
    76,
    82,
    88,
    142,
    148,
    154,
    160,
    166,
    172,
    178,
    184,
    189
   ],
   [
    47,
    53,
    59,
    65,
    71,
    77,
    83,
    89,
    143,
    149,
    155,
    161,
    167,
    173,
    179,
    185,
    189
   ],
   [
    90,
    96,
    102,
    108,
    114,
    120,
    126,
    132,
    138,
    144,
    150,
    156,
    162,
    168,
    174,
    180
   ],
   [
    91,
    97,
    103,
    109,
    115,
    121,
    127,
    133,
    139,
    145,
    151,
    157,
    163,
    169,
    175,
    181
   ],
   [
    92,
    98,
    104,
    110,
    116,
    122,
    128,
    134,
    140,
    146,
    152,
    158,
    164,
    170,
    176,
    182
   ],
   [
    93,
    99,
    105,
    111,
    117,
    123,
    129,
    135,
    141,
    147,
    153,
    159,
    165,
    171,
    177,
    183
   ],
   [
    94,
    100,
    106,
    112,
    118,
    124,
    130,
    136,
    142,
    148,
    154,
    160,
    166,
    172,
    178,
    184
   ],
   [
    95,
    101,
    107,
    113,
    119,
    125,
    131,
    137,
    143,
    149,
    155,
    161,
    167,
    173,
    179,
    185
   ]
  ],
  "Z": [
   [
    1,
    3,
    5,
    115,
    117,
    119,
    121,
    123,
    125
   ],
   [
    2,
    3,
    4,
    5,
    186
   ],
   [
    7,
    9,
    11,
    67,
    69,
    71,
    79,
    81,
    83
   ],
   [
    6,
    7,
    10,
    11,
    187
   ],
   [
    13,
    15,
    17,
    67,
    69,
    71,
    79,
    81,
    83,
    115,
    117,
    119,
    121,
    123,
    125
   ],
   [
    0,
    1,
    4,
    5,
    12,
    13,
    16,
    17,
    187
   ],
   [
    8,
    9,
    10,
    11,
    14,
    15,
    16,
    17,
    186
   ],
   [
    19,
    21,
    23,
    67,
    69,
    71,
    115,
    117,
    119,
    163,
    165,
    167
   ],
   [
    18,
    19,
    22,
    23,
    188
   ],
   [
    20,
    21,
    22,
    23,
    68,
    69,
    70,
    71,
    189
   ],
   [
    25,
    27,
    29,
    67,
    69,
    71,
    121,
    123,
    125,
    163,
    165,
    167
   ],
   [
    0,
    1,
    4,
    5,
    24,
    25,
    28,
    29,
    188
   ],
   [
    26,
    27,
    28,
    29,
    68,
    69,
    70,
    71,
    186,
    189
   ],
   [
    31,
    33,
    35,
    79,
    81,
    83,
    115,
    117,
    119,
    163,
    165,
    167
   ],
   [
    30,
    31,
    34,
    35,
    187,
    188
   ],
   [
    8,
    9,
    10,
    11,
    32,
    33,
    34,
    35,
    68,
    69,
    70,
    71,
    189
   ],
   [
    37,
    39,
    41,
    79,
    81,
    83,
    121,
    123,
    125,
    163,
    165,
    167
   ],
   [
    0,
    1,
    4,
    5,
    36,
    37,
    40,
    41,
    187,
    188
   ],
   [
    8,
    9,
    10,
    11,
    38,
    39,
    40,
    41,
    68,
    69,
    70,
    71,
    186,
    189
   ],
   [
    43,
    45,
    47,
    115,
    117,
    119,
    163,
    165,
    167
   ],
   [
    42,
    43,
    46,
    47,
    66,
    67,
    70,
    71,
    188
   ],
   [
    44,
    45,
    46,
    47,
    189
   ],
   [
    49,
    51,
    53,
    121,
    123,
    125,
    163,
    165,
    167
   ],
   [
    0,
    1,
    4,
    5,
    48,
    49,
    52,
    53,
    66,
    67,
    70,
    71,
    188
   ],
   [
    50,
    51,
    52,
    53,
    186,
    189
   ],
   [
    55,
    57,
    59,
    67,
    69,
    71,
    79,
    81,
    83,
    115,
    117,
    119,
    163,
    165,
    167
   ],
   [
    54,
    55,
    58,
    59,
    66,
    67,
    70,
    71,
    187,
    188
   ],
   [
    8,
    9,
    10,
    11,
    56,
    57,
    58,
    59,
    189
   ],
   [
    61,
    63,
    65,
    67,
    69,
    71,
    79,
    81,
    83,
    121,
    123,
    125,
    163,
    165,
    167
   ],
   [
    0,
    1,
    4,
    5,
    60,
    61,
    64,
    65,
    66,
    67,
    70,
    71,
    187,
    188
   ],
   [
    8,
    9,
    10,
    11,
    62,
    63,
    64,
    65,
    186,
    189
   ],
   [
    67,
    69,
    71,
    73,
    75,
    77,
    115,
    117,
    119,
    121,
    123,
    125
   ],
   [
    0,
    1,
    4,
    5,
    66,
    67,
    70,
    71,
    72,
    73,
    76,
    77
   ],
   [
    68,
    69,
    70,
    71,
    74,
    75,
    76,
    77,
    186
   ],
   [
    66,
    67,
    70,
    71,
    78,
    79,
    82,
    83,
    187
   ],
   [
    8,
    9,
    10,
    11,
    68,
    69,
    70,
    71,
    80,
    81,
    82,
    83
   ],
   [
    79,
    81,
    83,
    85,
    87,
    89,
    115,
    117,
    119,
    121,
    123,
    125
   ],
   [
    0,
    1,
    4,
    5,
    66,
    67,
    70,
    71,
    84,
    85,
    88,
    89,
    187
   ],
   [
    8,
    9,
    10,
    11,
    68,
    69,
    70,
    71,
    86,
    87,
    88,
    89,
    186
   ],
   [
    79,
    81,
    83,
    91,
    93,
    95,
    175,
    177,
    179
   ],
   [
    0,
    1,
    4,
    5,
    90,
    91,
    94,
    95,
    108,
    109,
    112,
    113,
    187
   ],
   [
    92,
    93,
    94,
    95,
    146,
    147,
    148,
    149,
    186,
    189
   ],
   [
    79,
    81,
    83,
    97,
    99,
    101,
    115,
    117,
    119,
    121,
    123,
    125,
    175,
    177,
    179
   ],
   [
    96,
    97,
    100,
    101,
    108,
    109,
    112,
    113,
    187
   ],
   [
    98,
    99,
    100,
    101,
    146,
    147,
    148,
    149,
    189
   ],
   [
    67,
    69,
    71,
    103,
    105,
    107,
    175,
    177,
    179
   ],
   [
    0,
    1,
    4,
    5,
    102,
    103,
    106,
    107,
    108,
    109,
    112,
    113
   ],
   [
    8,
    9,
    10,
    11,
    104,
    105,
    106,
    107,
    146,
    147,
    148,
    149,
    186,
    189
   ],
   [
    67,
    69,
    71,
    109,
    111,
    113,
    115,
    117,
    119,
    121,
    123,
    125,
    175,
    177,
    179
   ],
   [
    8,
    9,
    10,
    11,
    110,
    111,
    112,
    113,
    146,
    147,
    148,
    149,
    189
   ],
   [
    0,
    1,
    4,
    5,
    108,
    109,
    112,
    113,
    114,
    115,
    118,
    119,
    187,
    188
   ],
   [
    68,
    69,
    70,
    71,
    116,
    117,
    118,
    119,
    146,
    147,
    148,
    149,
    186
   ],
   [
    108,
    109,
    112,
    113,
    120,
    121,
    124,
    125,
    187,
    188
   ],
   [
    68,
    69,
    70,
    71,
    122,
    123,
    124,
    125,
    146,
    147,
    148,
    149
   ],
   [
    115,
    117,
    119,
    127,
    129,
    131,
    163,
    165,
    167,
    175,
    177,
    179
   ],
   [
    0,
    1,
    4,
    5,
    108,
    109,
    112,
    113,
    126,
    127,
    130,
    131,
    188
   ],
   [
    8,
    9,
    10,
    11,
    68,
    69,
    70,
    71,
    128,
    129,
    130,
    131,
    146,
    147,
    148,
    149,
    186
   ],
   [
    121,
    123,
    125,
    133,
    135,
    137,
    163,
    165,
    167,
    175,
    177,
    179
   ],
   [
    108,
    109,
    112,
    113,
    132,
    133,
    136,
    137,
    188
   ],
   [
    8,
    9,
    10,
    11,
    68,
    69,
    70,
    71,
    134,
    135,
    136,
    137,
    146,
    147,
    148,
    149
   ],
   [
    79,
    81,
    83,
    115,
    117,
    119,
    139,
    141,
    143,
    163,
    165,
    167,
    175,
    177,
    179
   ],
   [
    0,
    1,
    4,
    5,
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    138,
    139,
    142,
    143,
    187,
    188
   ],
   [
    140,
    141,
    142,
    143,
    146,
    147,
    148,
    149,
    186
   ],
   [
    79,
    81,
    83,
    121,
    123,
    125,
    145,
    147,
    149,
    163,
    165,
    167,
    175,
    177,
    179
   ],
   [
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    144,
    145,
    148,
    149,
    187,
    188
   ],
   [
    67,
    69,
    71,
    115,
    117,
    119,
    151,
    153,
    155,
    163,
    165,
    167,
    175,
    177,
    179
   ],
   [
    0,
    1,
    4,
    5,
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    150,
    151,
    154,
    155,
    188
   ],
   [
    8,
    9,
    10,
    11,
    146,
    147,
    148,
    149,
    152,
    153,
    154,
    155,
    186
   ],
   [
    67,
    69,
    71,
    121,
    123,
    125,
    157,
    159,
    161,
    163,
    165,
    167,
    175,
    177,
    179
   ],
   [
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    156,
    157,
    160,
    161,
    188
   ],
   [
    8,
    9,
    10,
    11,
    146,
    147,
    148,
    149,
    158,
    159,
    160,
    161
   ],
   [
    67,
    69,
    71,
    79,
    81,
    83,
    163,
    165,
    167,
    175,
    177,
    179
   ],
   [
    0,
    1,
    4,
    5,
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    162,
    163,
    166,
    167,
    187
   ],
   [
    68,
    69,
    70,
    71,
    146,
    147,
    148,
    149,
    164,
    165,
    166,
    167,
    186,
    189
   ],
   [
    67,
    69,
    71,
    79,
    81,
    83,
    115,
    117,
    119,
    121,
    123,
    125,
    169,
    171,
    173,
    175,
    177,
    179
   ],
   [
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    168,
    169,
    172,
    173,
    187
   ],
   [
    68,
    69,
    70,
    71,
    146,
    147,
    148,
    149,
    170,
    171,
    172,
    173,
    189
   ],
   [
    0,
    1,
    4,
    5,
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    174,
    175,
    178,
    179
   ],
   [
    8,
    9,
    10,
    11,
    68,
    69,
    70,
    71,
    146,
    147,
    148,
    149,
    176,
    177,
    178,
    179,
    186,
    189
   ],
   [
    115,
    117,
    119,
    121,
    123,
    125,
    175,
    177,
    179,
    181,
    183,
    185
   ],
   [
    66,
    67,
    70,
    71,
    108,
    109,
    112,
    113,
    180,
    181,
    184,
    185
   ],
   [
    8,
    9,
    10,
    11,
    68,
    69,
    70,
    71,
    146,
    147,
    148,
    149,
    182,
    183,
    184,
    185,
    189
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    175,
    176,
    179
   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-15",
    "found_at_samples": 20000,
    "survived_samples": 20000000,
    "tool": "gf2_fast RIS ladder (verify/gf2_fast.cpp), both sides searched jointly",
    "seeds": [
     777001,
     777138,
     777275,
     777412,
     777549
    ]
   }
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    17,
    149,
    155
   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-15",
    "found_at_samples": 4000,
    "survived_samples": 20000000,
    "tool": "gf2_fast RIS in the packaging search; the ladder searched both sides jointly",
    "seeds": [
     7,
     777001,
     777138,
     777275,
     777412,
     777549
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@dorakingx"
  ],
  "construction": "Reduction of the board's codes/201-78-3.json ([[201,78,3]]) by 11 qubits at unchanged k, unchanged check-weight class and unchanged locality class, by one move applied to a fixpoint: graft a qubit away using a low-weight element of the stabilizer ROW SPACE. Let S be an element of the row space of H_X with support T and let a be in T. Replace one generator of the subset summing to S by S itself -- the span is unchanged, that generator being S plus the rest of the subset -- and add S into every other X row meeting a, so that a survives only in S. Then apply the CNOT fan-out from a to T\\{a}, which acts on the check matrices as H_X[:, b] ^= H_X[:, a] and H_Z[:, a] ^= H_Z[:, b] for each b in T\\{a}. Only S still meets a, so the first substitution turns S into the weight-1 stabilizer X_a and leaves every other X row alone; the second zeroes column a of H_Z, because commutation forces every Z row to meet T an even number of times. Qubit a is then disentangled and is deleted: n -> n-1, k unchanged, and the Z rows only LOSE an index, so their weights and support diameters cannot rise. The weight of S separates three regimes, and the difference is entirely in the clearing step R ^= S. |S| = 1: nothing is added anywhere, so the weights, the radius AND THE DISTANCE are all preserved exactly, and no distance search is needed -- this is the row-space form of the weight-1 stabilizer cleanup of Liang, Eberhardt and Chen (arXiv:2504.08887 Sec. III D step 4), which the implementation in research/local2d/boundary_engine.py applies only to literal weight-1 generator ROWS. |S| = 2: R loses a and toggles one other index, so its weight changes by 0 or -2 and can never rise. |S| >= 3: R can grow, so every touched row is checked against the code's weight class and its locality radius, measured in the source's own layout. This generalises the capped merge-graft I introduced with [[454,8,17]], which only ever built S from the generators a single qubit happens to lie in. Here the accepted grafts were |S| = 5: 3, |S| = 6: 1, |S| = 7: 6, |S| = 8: 1. Low-weight row-space elements are enumerated as sums of at most three checks with a connected overlap pattern. Every graft with |S| >= 2 was accepted only if k was unchanged and a bit-packed RIS search found nothing lighter than 3, screened once and confirmed twice with independent seeds; those in-loop rungs are a filter, not the evidence. QUBIT POSITIONS ARE THE SOURCE'S: every surviving qubit keeps the coordinate it has in codes/201-78-3.json, so the layout is inherited rather than re-derived, and the reduction only deletes. The surviving qubits' indices into the source numbering are [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]... (full list implied by the coordinates in this file).",
  "references": [
   "arXiv:2504.08887"
  ],
  "date": "2026-09-15",
  "notes": "Derived from codes/201-78-3.json, not an independent construction; the source's authors are @mathysrennela and the reduction is mine. The gate reports no exact duplicate and no WL-equivalent entry. It dominates [[201,78,3]] on (n, k, d, w), which therefore leaves the frontier of every cell the two share. Distance is a witness-backed upper bound: the deepest null result is 20000000 fresh-seed RIS trials. Literature novelty is unverified.",
  "model": "Claude Opus 5 (Claude Code)",
  "origin": "submission",
  "novelty": "unknown"
 },
 "family": "hypergraph-product"
}