{
 "schema_version": "0.2",
 "name": "[[236,16,12]] reduction of [[261,16,12]]",
 "code_type": "CSS",
 "n": 236,
 "k": 16,
 "checks": {
  "X": [
   [
    0,
    13,
    22,
    25,
    142,
    149
   ],
   [
    14,
    23,
    26,
    122,
    143,
    150
   ],
   [
    1,
    16,
    25,
    28,
    124,
    145,
    152
   ],
   [
    2,
    17,
    26,
    29,
    120,
    125,
    146,
    153
   ],
   [
    3,
    18,
    27,
    30,
    121,
    126,
    147,
    154
   ],
   [
    4,
    19,
    28,
    31,
    127,
    148,
    155
   ],
   [
    6,
    22,
    32,
    35,
    122,
    123,
    151
   ],
   [
    5,
    23,
    33,
    36,
    123,
    130,
    152,
    159
   ],
   [
    6,
    24,
    34,
    37,
    124,
    131,
    153,
    160
   ],
   [
    7,
    25,
    35,
    38,
    125,
    132,
    154,
    161
   ],
   [
    8,
    26,
    36,
    39,
    126,
    133,
    155,
    162
   ],
   [
    9,
    27,
    37,
    40,
    127,
    134,
    156,
    163
   ],
   [
    10,
    28,
    38,
    41,
    128,
    135,
    157,
    164
   ],
   [
    11,
    29,
    39,
    42,
    129,
    136,
    158,
    165
   ],
   [
    13,
    33,
    43,
    46,
    131,
    139,
    161
   ],
   [
    14,
    34,
    44,
    47,
    132,
    140,
    162,
    168
   ],
   [
    15,
    35,
    45,
    48,
    133,
    141,
    163,
    169
   ],
   [
    16,
    36,
    46,
    49,
    134,
    142,
    164,
    170
   ],
   [
    17,
    37,
    47,
    50,
    135,
    143,
    165,
    171
   ],
   [
    18,
    38,
    48,
    51,
    136,
    144,
    166,
    172
   ],
   [
    19,
    39,
    49,
    52,
    137,
    145,
    167,
    173
   ],
   [
    24,
    45,
    53,
    56,
    142,
    150,
    171,
    178
   ],
   [
    25,
    46,
    54,
    57,
    143,
    151,
    172,
    179
   ],
   [
    26,
    47,
    55,
    58,
    144,
    152,
    173,
    180
   ],
   [
    27,
    48,
    56,
    59,
    145,
    153,
    174,
    181
   ],
   [
    28,
    49,
    57,
    60,
    146,
    154,
    175,
    182
   ],
   [
    29,
    50,
    58,
    61,
    147,
    155,
    176,
    183
   ],
   [
    30,
    51,
    59,
    62,
    148,
    156,
    177,
    184
   ],
   [
    34,
    53,
    63,
    66,
    151,
    159,
    180
   ],
   [
    35,
    54,
    64,
    67,
    152,
    160,
    181,
    188
   ],
   [
    36,
    55,
    65,
    68,
    153,
    161,
    182,
    189
   ],
   [
    37,
    56,
    66,
    69,
    154,
    162,
    183,
    190
   ],
   [
    38,
    57,
    67,
    70,
    155,
    163,
    184,
    191
   ],
   [
    39,
    58,
    68,
    71,
    156,
    164,
    185,
    192
   ],
   [
    40,
    59,
    69,
    72,
    157,
    165,
    186,
    193
   ],
   [
    41,
    60,
    70,
    158,
    166,
    187,
    194
   ],
   [
    45,
    64,
    73,
    76,
    161,
    168,
    190
   ],
   [
    46,
    65,
    74,
    77,
    162,
    169,
    191,
    198
   ],
   [
    47,
    66,
    75,
    78,
    163,
    170,
    192,
    199
   ],
   [
    48,
    67,
    76,
    79,
    164,
    171,
    193,
    200
   ],
   [
    49,
    68,
    77,
    80,
    165,
    172,
    194,
    201
   ],
   [
    50,
    69,
    78,
    81,
    166,
    173,
    195,
    202
   ],
   [
    51,
    70,
    79,
    82,
    167,
    174,
    196,
    203
   ],
   [
    54,
    74,
    83,
    86,
    170,
    178,
    200,
    208
   ],
   [
    55,
    75,
    84,
    87,
    171,
    179,
    201,
    209
   ],
   [
    56,
    76,
    85,
    88,
    172,
    180,
    202,
    210
   ],
   [
    57,
    77,
    86,
    89,
    173,
    181,
    203,
    211
   ],
   [
    58,
    78,
    87,
    90,
    174,
    182,
    204,
    212
   ],
   [
    59,
    79,
    88,
    91,
    175,
    183,
    205,
    213
   ],
   [
    60,
    80,
    89,
    92,
    176,
    184,
    206,
    214
   ],
   [
    61,
    81,
    90,
    177,
    185,
    207,
    215
   ],
   [
    65,
    84,
    93,
    96,
    180,
    188,
    211,
    218
   ],
   [
    66,
    85,
    94,
    97,
    181,
    189,
    212,
    219
   ],
   [
    67,
    86,
    95,
    98,
    182,
    190,
    213,
    220
   ],
   [
    68,
    87,
    96,
    99,
    183,
    191,
    214,
    221
   ],
   [
    69,
    88,
    97,
    100,
    184,
    192,
    215,
    222
   ],
   [
    70,
    89,
    98,
    101,
    185,
    193,
    216,
    223
   ],
   [
    71,
    90,
    99,
    102,
    186,
    194,
    217,
    224
   ],
   [
    72,
    91,
    100,
    187,
    195,
    225
   ],
   [
    75,
    94,
    103,
    106,
    190,
    198,
    221,
    227
   ],
   [
    76,
    95,
    104,
    107,
    191,
    199,
    222,
    228
   ],
   [
    77,
    96,
    105,
    108,
    192,
    200,
    223,
    229
   ],
   [
    78,
    97,
    106,
    109,
    193,
    201,
    224,
    230
   ],
   [
    79,
    98,
    107,
    110,
    194,
    202,
    225,
    231
   ],
   [
    82,
    101,
    110,
    112,
    197,
    205,
    226,
    234
   ],
   [
    2,
    123
   ],
   [
    0,
    7,
    124,
    130
   ],
   [
    5,
    8,
    125,
    131
   ],
   [
    6,
    9,
    126,
    132
   ],
   [
    1,
    7,
    10,
    127,
    133
   ],
   [
    2,
    8,
    11,
    128,
    134
   ],
   [
    9,
    17,
    20,
    137,
    144
   ],
   [
    12,
    21,
    24,
    141
   ],
   [
    15,
    24,
    27,
    123,
    144,
    151
   ],
   [
    0,
    1,
    122
   ],
   [
    3,
    120,
    124
   ],
   [
    1,
    4,
    121,
    125
   ],
   [
    12,
    15,
    132,
    139
   ],
   [
    5,
    13,
    16,
    133,
    140
   ],
   [
    6,
    14,
    17,
    134,
    141
   ],
   [
    7,
    15,
    18,
    135,
    142
   ],
   [
    8,
    16,
    19,
    136,
    143
   ],
   [
    10,
    18,
    120,
    138,
    145
   ],
   [
    110,
    116
   ],
   [
    98,
    115,
    214,
    222
   ],
   [
    99,
    116,
    215,
    223
   ],
   [
    80,
    99,
    108,
    111,
    195,
    203,
    232
   ],
   [
    117,
    234
   ],
   [
    111,
    117
   ],
   [
    107,
    223,
    230
   ],
   [
    108,
    224,
    231
   ],
   [
    109,
    225,
    232
   ],
   [
    110,
    233
   ],
   [
    111,
    234
   ],
   [
    81,
    100,
    109,
    196,
    204,
    226,
    233,
    235
   ],
   [
    96,
    212,
    220,
    230
   ],
   [
    97,
    213,
    221,
    231
   ],
   [
    115,
    232
   ],
   [
    116,
    233
   ],
   [
    100,
    216,
    224,
    234
   ],
   [
    101,
    217,
    225,
    235
   ],
   [
    105,
    221,
    228
   ],
   [
    106,
    222,
    229
   ],
   [
    95,
    114,
    211,
    219
   ],
   [
    85,
    104,
    113,
    200,
    209,
    230,
    231
   ],
   [
    86,
    105,
    114,
    115,
    201,
    210,
    231
   ],
   [
    87,
    106,
    116,
    202,
    211,
    230,
    232
   ],
   [
    88,
    107,
    117,
    203,
    212,
    231,
    233
   ],
   [
    89,
    108,
    115,
    204,
    213,
    234,
    235
   ],
   [
    90,
    102,
    109,
    116,
    205,
    214,
    235
   ],
   [
    91,
    102,
    110,
    117,
    118,
    206,
    215
   ],
   [
    92,
    111,
    118,
    119,
    207,
    216,
    235
   ],
   [
    84,
    103,
    199,
    208,
    227,
    229,
    230
   ],
   [
    94,
    113,
    210,
    218
   ],
   [
    104,
    220,
    227
   ]
  ],
  "Z": [
   [
    0,
    23,
    32,
    122,
    130,
    149
   ],
   [
    1,
    5,
    26,
    35,
    122,
    125,
    133,
    152
   ],
   [
    2,
    6,
    27,
    36,
    123,
    126,
    134,
    153
   ],
   [
    3,
    7,
    28,
    37,
    124,
    127,
    135,
    154
   ],
   [
    4,
    8,
    29,
    38,
    125,
    128,
    136,
    155
   ],
   [
    9,
    30,
    39,
    126,
    129,
    137,
    156
   ],
   [
    6,
    12,
    35,
    44,
    132,
    141,
    160
   ],
   [
    7,
    13,
    36,
    45,
    130,
    133,
    142,
    161
   ],
   [
    8,
    14,
    37,
    46,
    131,
    134,
    143,
    162
   ],
   [
    9,
    15,
    38,
    47,
    132,
    135,
    144,
    163
   ],
   [
    10,
    16,
    39,
    48,
    133,
    136,
    145,
    164
   ],
   [
    11,
    17,
    40,
    49,
    134,
    137,
    146,
    165
   ],
   [
    18,
    41,
    50,
    135,
    138,
    147,
    166
   ],
   [
    14,
    21,
    45,
    141,
    150,
    168
   ],
   [
    15,
    22,
    46,
    53,
    139,
    142,
    151,
    169
   ],
   [
    16,
    23,
    47,
    54,
    140,
    143,
    152,
    170
   ],
   [
    17,
    24,
    48,
    55,
    141,
    144,
    153,
    171
   ],
   [
    18,
    25,
    49,
    56,
    142,
    145,
    154,
    172
   ],
   [
    19,
    26,
    50,
    57,
    143,
    146,
    155,
    173
   ],
   [
    20,
    27,
    51,
    58,
    144,
    147,
    156,
    174
   ],
   [
    21,
    24,
    32,
    54,
    63,
    151,
    160,
    178
   ],
   [
    25,
    33,
    55,
    64,
    149,
    152,
    161,
    179
   ],
   [
    26,
    34,
    56,
    65,
    150,
    153,
    162,
    180
   ],
   [
    27,
    35,
    57,
    66,
    151,
    154,
    163,
    181
   ],
   [
    28,
    36,
    58,
    67,
    152,
    155,
    164,
    182
   ],
   [
    29,
    37,
    59,
    68,
    153,
    156,
    165,
    183
   ],
   [
    30,
    38,
    60,
    69,
    154,
    157,
    166,
    184
   ],
   [
    31,
    39,
    61,
    70,
    155,
    158,
    167,
    185
   ],
   [
    32,
    35,
    43,
    65,
    73,
    161,
    169,
    188
   ],
   [
    36,
    44,
    66,
    74,
    159,
    162,
    170,
    189
   ],
   [
    37,
    45,
    67,
    75,
    160,
    163,
    171,
    190
   ],
   [
    38,
    46,
    68,
    76,
    161,
    164,
    172,
    191
   ],
   [
    39,
    47,
    69,
    77,
    162,
    165,
    173,
    192
   ],
   [
    40,
    48,
    70,
    78,
    163,
    166,
    174,
    193
   ],
   [
    41,
    49,
    71,
    79,
    164,
    167,
    175,
    194
   ],
   [
    42,
    50,
    72,
    80,
    165,
    176,
    195
   ],
   [
    47,
    53,
    76,
    84,
    168,
    171,
    180,
    199
   ],
   [
    48,
    54,
    77,
    85,
    169,
    172,
    181,
    200
   ],
   [
    49,
    55,
    78,
    86,
    170,
    173,
    182,
    201
   ],
   [
    50,
    56,
    79,
    87,
    171,
    174,
    183,
    202
   ],
   [
    51,
    57,
    80,
    88,
    172,
    175,
    184,
    203
   ],
   [
    52,
    58,
    81,
    89,
    173,
    176,
    185,
    204
   ],
   [
    59,
    82,
    90,
    174,
    177,
    186,
    205
   ],
   [
    55,
    63,
    85,
    93,
    180,
    189,
    209
   ],
   [
    56,
    64,
    86,
    94,
    178,
    181,
    190,
    210
   ],
   [
    57,
    65,
    87,
    95,
    179,
    182,
    191,
    211
   ],
   [
    58,
    66,
    88,
    96,
    180,
    183,
    192,
    212
   ],
   [
    59,
    67,
    89,
    97,
    181,
    184,
    193,
    213
   ],
   [
    60,
    68,
    90,
    98,
    182,
    185,
    194,
    214
   ],
   [
    61,
    69,
    91,
    99,
    183,
    186,
    195,
    215
   ],
   [
    62,
    70,
    92,
    100,
    184,
    187,
    196,
    216
   ],
   [
    63,
    66,
    73,
    95,
    103,
    190,
    199,
    219
   ],
   [
    67,
    74,
    96,
    104,
    188,
    191,
    200,
    220
   ],
   [
    68,
    75,
    97,
    105,
    189,
    192,
    201,
    221
   ],
   [
    69,
    76,
    98,
    106,
    190,
    193,
    202,
    222
   ],
   [
    70,
    77,
    99,
    107,
    191,
    194,
    203,
    223
   ],
   [
    71,
    78,
    100,
    108,
    192,
    195,
    204,
    224
   ],
   [
    72,
    79,
    101,
    109,
    193,
    196,
    205,
    225
   ],
   [
    73,
    76,
    83,
    105,
    113,
    200,
    210,
    228
   ],
   [
    77,
    84,
    106,
    114,
    198,
    201,
    211,
    229
   ],
   [
    78,
    85,
    107,
    199,
    202,
    212,
    230
   ],
   [
    79,
    86,
    108,
    200,
    203,
    213,
    231
   ],
   [
    80,
    87,
    109,
    115,
    201,
    204,
    214,
    232
   ],
   [
    81,
    88,
    110,
    116,
    202,
    205,
    215,
    233
   ],
   [
    82,
    89,
    111,
    117,
    203,
    206,
    216,
    234
   ],
   [
    90,
    204,
    207,
    217,
    235
   ],
   [
    12,
    21,
    43,
    139
   ],
   [
    22,
    32,
    149
   ],
   [
    33,
    43,
    63,
    159
   ],
   [
    44,
    73,
    168
   ],
   [
    53,
    63,
    83,
    178
   ],
   [
    64,
    73,
    93,
    188
   ],
   [
    74,
    103,
    198,
    208
   ],
   [
    13,
    43,
    44,
    140,
    149
   ],
   [
    34,
    63,
    64,
    160,
    168
   ],
   [
    45,
    73,
    74,
    169,
    178
   ],
   [
    5,
    34,
    43,
    131,
    140,
    159
   ],
   [
    43,
    46,
    75,
    83,
    170,
    179,
    198
   ],
   [
    23,
    53,
    150,
    159
   ],
   [
    54,
    84,
    179,
    188,
    208
   ],
   [
    65,
    94,
    189,
    198,
    218
   ],
   [
    75,
    104,
    199,
    209,
    227
   ],
   [
    42,
    129
   ],
   [
    28,
    52,
    59,
    138,
    145,
    148,
    157,
    175
   ],
   [
    31,
    62,
    148
   ],
   [
    112,
    197
   ],
   [
    62,
    119,
    177,
    207
   ],
   [
    11,
    41,
    128,
    158
   ],
   [
    20,
    52,
    137
   ],
   [
    30,
    61,
    147,
    177
   ],
   [
    41,
    72,
    157,
    187
   ],
   [
    52,
    82,
    167,
    197
   ],
   [
    61,
    92,
    176,
    207
   ],
   [
    82,
    196,
    226
   ],
   [
    92,
    118,
    206
   ],
   [
    10,
    31,
    40,
    127,
    138,
    157
   ],
   [
    19,
    42,
    51,
    136,
    148,
    167
   ],
   [
    29,
    60,
    146,
    158,
    176
   ],
   [
    40,
    62,
    71,
    156,
    186
   ],
   [
    42,
    51,
    81,
    158,
    166,
    177,
    196
   ],
   [
    60,
    91,
    175,
    187,
    206
   ],
   [
    62,
    71,
    101,
    177,
    185,
    197,
    217
   ],
   [
    72,
    91,
    102,
    112,
    186,
    205
   ],
   [
    4,
    30,
    121,
    148
   ],
   [
    3,
    29,
    120,
    129,
    138,
    147
   ],
   [
    83,
    84,
    113,
    208,
    209,
    218
   ],
   [
    85,
    113,
    114,
    210,
    219
   ]
  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    2,
    6,
    24,
    25,
    56,
    64,
    93,
    96,
    160,
    171,
    180,
    220
   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-11",
    "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": 12,
   "confidence": "upper_bound",
   "witness": [
    6,
    9,
    11,
    20,
    32,
    42,
    43,
    46,
    54,
    74,
    134,
    160
   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-11",
    "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/261-16-12.json ([[261,16,12]]) by 25 qubits at unchanged k and check-weight class, using three moves. (1) Restricted r=1 lattice grafting (Liang, Eberhardt, Chen, arXiv:2504.08887, Sec. III E): a qubit lying in exactly one stabilizer of some type is removed together with that stabilizer, which preserves CSS commutation automatically because no other same-type row touches it. (2) Weight-1 stabilizer cleanup (Sec. III D step 4, research/local2d/boundary_engine.py _cleanup), which runs no distance search because it needs none: a qubit carrying a weight-1 stabilizer cannot appear in any opposite-type check, so multiplying that row into the same-type rows containing it and deleting the qubit preserves k and the distance exactly. (3) Capped merge-graft, new here: when a qubit lies in exactly r <= 3 stabilizers of one type, pick a pivot row R_p and replace every other R_i by R_p + R_i -- row operations on the stabilizer generators, so the code is unchanged and only the generating set moves -- after which the qubit sits in R_p alone and move (1) applies. Every choice of pivot is tried, since each gives a different resulting code. Unlike the first two moves this one can enlarge a check, so every merged row is accepted only if it still has weight at most 8 and, in the source's own layout, a support diameter within the locality class's cap; the whole layout radius is re-measured after every accepted move. Acceptance also requires k unchanged and a bit-packed RIS search finding nothing lighter than 12, screened then confirmed at a deeper rung. Those in-loop rungs are a filter, not the evidence: the claim below rests on the separate fresh-seed ladder. QUBIT POSITIONS ARE THE SOURCE'S: every surviving qubit keeps the coordinate it has in codes/261-16-12.json, so the layout is inherited rather than re-derived, and the reduction only deletes. The surviving qubits' indices into the source numbering are [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]... (full list implied by the coordinates in this file).",
  "references": [
   "arXiv:2504.08887"
  ],
  "date": "2026-09-11",
  "notes": "Derived from codes/261-16-12.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 [[240,12,12]], [[242,12,12]], [[261,16,12]], [[263,16,12]] on (n, k, d, w), which therefore leave the frontier of every cell they share with it. The measured interaction radius is 6, against 5 for the source: unlike the graft and the cleanup, the merge-graft can widen a check, and it is capped by the locality class rather than by the source's own radius, so the reduced code is less local even though it stays in the same cell. 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": "bivariate-bicycle",
 "locality": {
  "coordinates": [
   [
    0.0,
    3.0
   ],
   [
    0.0,
    6.0
   ],
   [
    0.0,
    7.0
   ],
   [
    0.0,
    8.0
   ],
   [
    0.0,
    9.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    4.0
   ],
   [
    1.0,
    5.0
   ],
   [
    1.0,
    6.0
   ],
   [
    1.0,
    7.0
   ],
   [
    1.0,
    8.0
   ],
   [
    1.0,
    9.0
   ],
   [
    2.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    4.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    6.0
   ],
   [
    2.0,
    7.0
   ],
   [
    2.0,
    8.0
   ],
   [
    2.0,
    9.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    4.0
   ],
   [
    3.0,
    5.0
   ],
   [
    3.0,
    6.0
   ],
   [
    3.0,
    7.0
   ],
   [
    3.0,
    8.0
   ],
   [
    3.0,
    9.0
   ],
   [
    3.0,
    10.0
   ],
   [
    4.0,
    0.0
   ],
   [
    4.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    4.0,
    4.0
   ],
   [
    4.0,
    5.0
   ],
   [
    4.0,
    6.0
   ],
   [
    4.0,
    7.0
   ],
   [
    4.0,
    8.0
   ],
   [
    4.0,
    9.0
   ],
   [
    4.0,
    10.0
   ],
   [
    5.0,
    0.0
   ],
   [
    5.0,
    1.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    4.0
   ],
   [
    5.0,
    5.0
   ],
   [
    5.0,
    6.0
   ],
   [
    5.0,
    7.0
   ],
   [
    5.0,
    8.0
   ],
   [
    5.0,
    9.0
   ],
   [
    6.0,
    1.0
   ],
   [
    6.0,
    2.0
   ],
   [
    6.0,
    3.0
   ],
   [
    6.0,
    4.0
   ],
   [
    6.0,
    5.0
   ],
   [
    6.0,
    6.0
   ],
   [
    6.0,
    7.0
   ],
   [
    6.0,
    8.0
   ],
   [
    6.0,
    9.0
   ],
   [
    6.0,
    10.0
   ],
   [
    7.0,
    0.0
   ],
   [
    7.0,
    1.0
   ],
   [
    7.0,
    2.0
   ],
   [
    7.0,
    3.0
   ],
   [
    7.0,
    4.0
   ],
   [
    7.0,
    5.0
   ],
   [
    7.0,
    6.0
   ],
   [
    7.0,
    7.0
   ],
   [
    7.0,
    8.0
   ],
   [
    7.0,
    9.0
   ],
   [
    8.0,
    0.0
   ],
   [
    8.0,
    1.0
   ],
   [
    8.0,
    2.0
   ],
   [
    8.0,
    3.0
   ],
   [
    8.0,
    4.0
   ],
   [
    8.0,
    5.0
   ],
   [
    8.0,
    6.0
   ],
   [
    8.0,
    7.0
   ],
   [
    8.0,
    8.0
   ],
   [
    8.0,
    9.0
   ],
   [
    9.0,
    0.0
   ],
   [
    9.0,
    1.0
   ],
   [
    9.0,
    2.0
   ],
   [
    9.0,
    3.0
   ],
   [
    9.0,
    4.0
   ],
   [
    9.0,
    5.0
   ],
   [
    9.0,
    6.0
   ],
   [
    9.0,
    7.0
   ],
   [
    9.0,
    8.0
   ],
   [
    9.0,
    9.0
   ],
   [
    10.0,
    0.0
   ],
   [
    10.0,
    1.0
   ],
   [
    10.0,
    2.0
   ],
   [
    10.0,
    3.0
   ],
   [
    10.0,
    4.0
   ],
   [
    10.0,
    5.0
   ],
   [
    10.0,
    6.0
   ],
   [
    10.0,
    7.0
   ],
   [
    10.0,
    8.0
   ],
   [
    10.0,
    9.0
   ],
   [
    11.0,
    0.0
   ],
   [
    11.0,
    1.0
   ],
   [
    11.0,
    2.0
   ],
   [
    11.0,
    3.0
   ],
   [
    11.0,
    4.0
   ],
   [
    11.0,
    5.0
   ],
   [
    11.0,
    6.0
   ],
   [
    11.0,
    7.0
   ],
   [
    11.0,
    8.0
   ],
   [
    11.0,
    10.0
   ],
   [
    12.0,
    0.0
   ],
   [
    12.0,
    1.0
   ],
   [
    12.0,
    4.0
   ],
   [
    12.0,
    5.0
   ],
   [
    12.0,
    6.0
   ],
   [
    12.0,
    9.0
   ],
   [
    12.0,
    10.0
   ],
   [
    0.0,
    8.0
   ],
   [
    0.0,
    9.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    4.0
   ],
   [
    1.0,
    5.0
   ],
   [
    1.0,
    6.0
   ],
   [
    1.0,
    7.0
   ],
   [
    1.0,
    8.0
   ],
   [
    1.0,
    9.0
   ],
   [
    1.0,
    10.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    4.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    6.0
   ],
   [
    2.0,
    7.0
   ],
   [
    2.0,
    8.0
   ],
   [
    2.0,
    9.0
   ],
   [
    2.0,
    10.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    4.0
   ],
   [
    3.0,
    5.0
   ],
   [
    3.0,
    6.0
   ],
   [
    3.0,
    7.0
   ],
   [
    3.0,
    8.0
   ],
   [
    3.0,
    9.0
   ],
   [
    3.0,
    10.0
   ],
   [
    4.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    4.0,
    4.0
   ],
   [
    4.0,
    5.0
   ],
   [
    4.0,
    6.0
   ],
   [
    4.0,
    7.0
   ],
   [
    4.0,
    8.0
   ],
   [
    4.0,
    9.0
   ],
   [
    4.0,
    10.0
   ],
   [
    5.0,
    1.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    4.0
   ],
   [
    5.0,
    5.0
   ],
   [
    5.0,
    6.0
   ],
   [
    5.0,
    7.0
   ],
   [
    5.0,
    8.0
   ],
   [
    5.0,
    9.0
   ],
   [
    6.0,
    1.0
   ],
   [
    6.0,
    2.0
   ],
   [
    6.0,
    3.0
   ],
   [
    6.0,
    4.0
   ],
   [
    6.0,
    5.0
   ],
   [
    6.0,
    6.0
   ],
   [
    6.0,
    7.0
   ],
   [
    6.0,
    8.0
   ],
   [
    6.0,
    9.0
   ],
   [
    6.0,
    10.0
   ],
   [
    7.0,
    1.0
   ],
   [
    7.0,
    2.0
   ],
   [
    7.0,
    3.0
   ],
   [
    7.0,
    4.0
   ],
   [
    7.0,
    5.0
   ],
   [
    7.0,
    6.0
   ],
   [
    7.0,
    7.0
   ],
   [
    7.0,
    8.0
   ],
   [
    7.0,
    9.0
   ],
   [
    7.0,
    10.0
   ],
   [
    8.0,
    1.0
   ],
   [
    8.0,
    2.0
   ],
   [
    8.0,
    3.0
   ],
   [
    8.0,
    4.0
   ],
   [
    8.0,
    5.0
   ],
   [
    8.0,
    6.0
   ],
   [
    8.0,
    7.0
   ],
   [
    8.0,
    8.0
   ],
   [
    8.0,
    9.0
   ],
   [
    8.0,
    10.0
   ],
   [
    9.0,
    1.0
   ],
   [
    9.0,
    2.0
   ],
   [
    9.0,
    3.0
   ],
   [
    9.0,
    4.0
   ],
   [
    9.0,
    5.0
   ],
   [
    9.0,
    6.0
   ],
   [
    9.0,
    7.0
   ],
   [
    9.0,
    8.0
   ],
   [
    9.0,
    9.0
   ],
   [
    9.0,
    10.0
   ],
   [
    10.0,
    0.0
   ],
   [
    10.0,
    1.0
   ],
   [
    10.0,
    2.0
   ],
   [
    10.0,
    3.0
   ],
   [
    10.0,
    4.0
   ],
   [
    10.0,
    5.0
   ],
   [
    10.0,
    6.0
   ],
   [
    10.0,
    7.0
   ],
   [
    10.0,
    8.0
   ],
   [
    10.0,
    9.0
   ],
   [
    11.0,
    0.0
   ],
   [
    11.0,
    1.0
   ],
   [
    11.0,
    2.0
   ],
   [
    11.0,
    3.0
   ],
   [
    11.0,
    4.0
   ],
   [
    11.0,
    5.0
   ],
   [
    11.0,
    6.0
   ],
   [
    11.0,
    7.0
   ],
   [
    11.0,
    10.0
   ],
   [
    12.0,
    0.0
   ],
   [
    12.0,
    1.0
   ],
   [
    12.0,
    2.0
   ],
   [
    12.0,
    3.0
   ],
   [
    12.0,
    4.0
   ],
   [
    12.0,
    5.0
   ],
   [
    12.0,
    6.0
   ],
   [
    12.0,
    7.0
   ],
   [
    12.0,
    8.0
   ]
  ],
  "interaction_radius": 6.0,
  "layers": 2
 }
}