{
 "schema_version": "0.1",
 "name": "[[60,4,8]] weight-5 two-block group-algebra code on MC(3,10,2), two-layer 2D-local layout",
 "code_type": "CSS",
 "n": 60,
 "k": 4,
 "checks": {
  "X": [
   [
    0,
    10,
    22,
    30,
    37
   ],
   [
    1,
    11,
    23,
    31,
    38
   ],
   [
    2,
    12,
    24,
    32,
    39
   ],
   [
    3,
    13,
    25,
    30,
    33
   ],
   [
    4,
    14,
    26,
    31,
    34
   ],
   [
    5,
    15,
    27,
    32,
    35
   ],
   [
    6,
    16,
    28,
    33,
    36
   ],
   [
    7,
    17,
    29,
    34,
    37
   ],
   [
    8,
    18,
    20,
    35,
    38
   ],
   [
    9,
    19,
    21,
    36,
    39
   ],
   [
    2,
    10,
    20,
    40,
    47
   ],
   [
    3,
    11,
    21,
    41,
    48
   ],
   [
    4,
    12,
    22,
    42,
    49
   ],
   [
    5,
    13,
    23,
    40,
    43
   ],
   [
    6,
    14,
    24,
    41,
    44
   ],
   [
    7,
    15,
    25,
    42,
    45
   ],
   [
    8,
    16,
    26,
    43,
    46
   ],
   [
    9,
    17,
    27,
    44,
    47
   ],
   [
    0,
    18,
    28,
    45,
    48
   ],
   [
    1,
    19,
    29,
    46,
    49
   ],
   [
    0,
    12,
    20,
    50,
    57
   ],
   [
    1,
    13,
    21,
    51,
    58
   ],
   [
    2,
    14,
    22,
    52,
    59
   ],
   [
    3,
    15,
    23,
    50,
    53
   ],
   [
    4,
    16,
    24,
    51,
    54
   ],
   [
    5,
    17,
    25,
    52,
    55
   ],
   [
    6,
    18,
    26,
    53,
    56
   ],
   [
    7,
    19,
    27,
    54,
    57
   ],
   [
    8,
    10,
    28,
    55,
    58
   ],
   [
    9,
    11,
    29,
    56,
    59
   ]
  ],
  "Z": [
   [
    0,
    3,
    30,
    48,
    50
   ],
   [
    1,
    4,
    31,
    49,
    51
   ],
   [
    2,
    5,
    32,
    40,
    52
   ],
   [
    3,
    6,
    33,
    41,
    53
   ],
   [
    4,
    7,
    34,
    42,
    54
   ],
   [
    5,
    8,
    35,
    43,
    55
   ],
   [
    6,
    9,
    36,
    44,
    56
   ],
   [
    0,
    7,
    37,
    45,
    57
   ],
   [
    1,
    8,
    38,
    46,
    58
   ],
   [
    2,
    9,
    39,
    47,
    59
   ],
   [
    10,
    13,
    30,
    40,
    58
   ],
   [
    11,
    14,
    31,
    41,
    59
   ],
   [
    12,
    15,
    32,
    42,
    50
   ],
   [
    13,
    16,
    33,
    43,
    51
   ],
   [
    14,
    17,
    34,
    44,
    52
   ],
   [
    15,
    18,
    35,
    45,
    53
   ],
   [
    16,
    19,
    36,
    46,
    54
   ],
   [
    10,
    17,
    37,
    47,
    55
   ],
   [
    11,
    18,
    38,
    48,
    56
   ],
   [
    12,
    19,
    39,
    49,
    57
   ],
   [
    20,
    23,
    38,
    40,
    50
   ],
   [
    21,
    24,
    39,
    41,
    51
   ],
   [
    22,
    25,
    30,
    42,
    52
   ],
   [
    23,
    26,
    31,
    43,
    53
   ],
   [
    24,
    27,
    32,
    44,
    54
   ],
   [
    25,
    28,
    33,
    45,
    55
   ],
   [
    26,
    29,
    34,
    46,
    56
   ],
   [
    20,
    27,
    35,
    47,
    57
   ],
   [
    21,
    28,
    36,
    48,
    58
   ],
   [
    22,
    29,
    37,
    49,
    59
   ]
  ]
 },
 "distance": {
  "d": 8,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    12,
    15,
    26,
    29,
    39,
    41,
    53,
    59
   ]
  },
  "Z": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    7,
    9,
    27,
    29,
    32,
    39,
    42,
    49
   ]
  }
 },
 "provenance": {
  "authors": [
   "@willzeng"
  ],
  "construction": "Two-block group-algebra (2BGA) code (Lin-Pryadko) on the non-abelian metacyclic group C_3 x| C_10 (action i -> 2^j i mod 3; kit group_algebra.metacyclic(3,10,2), element (i,j) at index i*10+j): a = {g_0, g_18, g_20} (element indices [0, 18, 20]), b = {g_0, g_3} (indices [0, 3]); H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T], so every check has weight 5. Found by a screen of all |a|=3, |b|=2 supports on small non-abelian groups ranked by kd^2/n; layout by simulated annealing on integer grid sites, <= 2 qubits per site.",
  "origin": "submission",
  "date": "2026-09-02",
  "model": "Claude Fable 5.1",
  "notes": "Distance is a witnessed UPPER BOUND (RIS witness search, 20000 Python trials plus a 2,000,000-trial accelerator pass at packaging; earlier confirmation ladders in notes/60-4-8.md); novelty vs the literature unverified. Equivalence check: verify/validate_candidate.py dedup found no identical or WL-equivalent entry on the board. Layout: simulated annealing over integer grid sites with at most 2 qubits per site (research/local2d/fold_layout.py::anneal), 2 layers, measured interaction radius 3.6056; the verifier derives the locality class. Search driven by Claude Fable 5.1 as one lane of a multi-agent campaign."
 },
 "family": "generalized-bicycle",
 "locality": {
  "coordinates": [
   [
    1.0,
    1.0
   ],
   [
    4.0,
    4.0
   ],
   [
    1.0,
    2.0
   ],
   [
    3.0,
    0.0
   ],
   [
    2.0,
    5.0
   ],
   [
    1.0,
    0.0
   ],
   [
    5.0,
    1.0
   ],
   [
    0.0,
    4.0
   ],
   [
    2.0,
    3.0
   ],
   [
    3.0,
    4.0
   ],
   [
    0.0,
    0.0
   ],
   [
    5.0,
    2.0
   ],
   [
    1.0,
    4.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    3.0
   ],
   [
    2.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    0.0,
    2.0
   ],
   [
    4.0,
    0.0
   ],
   [
    3.0,
    5.0
   ],
   [
    2.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    4.0,
    1.0
   ],
   [
    4.0,
    4.0
   ],
   [
    0.0,
    1.0
   ],
   [
    5.0,
    3.0
   ],
   [
    1.0,
    3.0
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    4.0
   ],
   [
    0.0,
    1.0
   ],
   [
    5.0,
    3.0
   ],
   [
    1.0,
    3.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    2.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    5.0,
    1.0
   ],
   [
    3.0,
    4.0
   ],
   [
    2.0,
    0.0
   ],
   [
    5.0,
    2.0
   ],
   [
    0.0,
    4.0
   ],
   [
    4.0,
    1.0
   ],
   [
    2.0,
    3.0
   ],
   [
    1.0,
    1.0
   ],
   [
    5.0,
    4.0
   ],
   [
    1.0,
    2.0
   ],
   [
    3.0,
    0.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    0.0,
    2.0
   ],
   [
    4.0,
    0.0
   ],
   [
    3.0,
    5.0
   ],
   [
    1.0,
    0.0
   ],
   [
    3.0,
    2.0
   ],
   [
    1.0,
    4.0
   ],
   [
    3.0,
    1.0
   ],
   [
    2.0,
    4.0
   ]
  ],
  "layers": 2
 }
}
