{
 "schema_version": "0.3",
 "name": "[[84,38,d]], self-dual PSL(2,7) hyperbolic surface code, {7,7} tiling",
 "code_type": "CSS",
 "n": 84,
 "k": 38,
 "checks": {
  "X": [
   [
    0,
    26,
    33,
    40,
    47,
    54,
    55
   ],
   [
    1,
    27,
    34,
    41,
    48,
    49,
    55
   ],
   [
    2,
    21,
    28,
    35,
    42,
    49,
    50
   ],
   [
    3,
    22,
    29,
    36,
    43,
    50,
    51
   ],
   [
    4,
    23,
    30,
    37,
    44,
    51,
    52
   ],
   [
    5,
    24,
    31,
    38,
    45,
    52,
    53
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   [
    6,
    25,
    32,
    39,
    46,
    53,
    54
   ],
   [
    7,
    27,
    42,
    62,
    66,
    69,
    76
   ],
   [
    8,
    24,
    46,
    56,
    63,
    67,
    70
   ],
   [
    9,
    21,
    43,
    57,
    64,
    68,
    71
   ],
   [
    10,
    25,
    47,
    58,
    65,
    69,
    72
   ],
   [
    11,
    22,
    44,
    59,
    63,
    66,
    73
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   [
    12,
    26,
    48,
    60,
    64,
    67,
    74
   ],
   [
    13,
    23,
    45,
    61,
    65,
    68,
    75
   ],
   [
    14,
    29,
    39,
    59,
    70,
    81,
    83
   ],
   [
    15,
    34,
    37,
    62,
    73,
    77,
    82
   ],
   [
    16,
    32,
    35,
    58,
    76,
    78,
    83
   ],
   [
    17,
    30,
    40,
    61,
    72,
    77,
    79
   ],
   [
    18,
    28,
    38,
    57,
    75,
    78,
    80
   ],
   [
    19,
    33,
    36,
    60,
    71,
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    81
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   [
    20,
    31,
    41,
    56,
    74,
    80,
    82
   ],
   [
    0,
    1,
    2,
    3,
    4,
    5,
    6
   ],
   [
    7,
    8,
    9,
    10,
    11,
    12,
    13
   ],
   [
    14,
    15,
    16,
    17,
    18,
    19,
    20
   ]
  ],
  "Z": [
   [
    0,
    2,
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    62,
    74,
    82
   ],
   [
    1,
    3,
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    76,
    78
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   [
    2,
    4,
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    44,
    59,
    71,
    81
   ],
   [
    3,
    5,
    22,
    45,
    61,
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   [
    4,
    6,
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    46,
    56,
    75,
    80
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   [
    0,
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    58,
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   [
    1,
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   ],
   [
    7,
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    37,
    51,
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   [
    8,
    9,
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    41,
    55,
    56,
    71
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   [
    9,
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    30,
    38,
    52,
    57,
    72
   ],
   [
    10,
    11,
    34,
    35,
    49,
    58,
    73
   ],
   [
    11,
    12,
    31,
    39,
    53,
    59,
    74
   ],
   [
    12,
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    28,
    36,
    50,
    60,
    75
   ],
   [
    7,
    13,
    32,
    40,
    54,
    61,
    76
   ],
   [
    14,
    17,
    26,
    29,
    40,
    43,
    64
   ],
   [
    15,
    18,
    24,
    34,
    38,
    48,
    67
   ],
   [
    16,
    19,
    22,
    32,
    36,
    46,
    63
   ],
   [
    17,
    20,
    27,
    30,
    41,
    44,
    66
   ],
   [
    14,
    18,
    25,
    28,
    39,
    42,
    69
   ],
   [
    15,
    19,
    23,
    33,
    37,
    47,
    65
   ],
   [
    16,
    20,
    21,
    31,
    35,
    45,
    68
   ],
   [
    49,
    50,
    51,
    52,
    53,
    54,
    55
   ],
   [
    63,
    64,
    65,
    66,
    67,
    68,
    69
   ],
   [
    77,
    78,
    79,
    80,
    81,
    82,
    83
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    5,
    77,
    83
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-10",
    "found_at_samples": 20000,
    "survived_samples": 20000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1
    ]
   }
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    10,
    13,
    65
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-10",
    "found_at_samples": 20000,
    "survived_samples": 20000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     2
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Regular {7,7} hyperbolic surface code on a closed orientable surface. Quotient Q = Delta_7/Gamma with Q = PSL(2,7); the face-vertex swap is a projective involution J in PGL(2,7) imposing y = J x J^-1, with ord(x) = ord(y) = 7 and ord(xy) = 2. Data qubits on edges = left cosets of the order-2 subgroup <xy>; Z checks on face boundaries = left cosets of <x>; X checks on vertex stars = left cosets of <y>. Checks commute because each face boundary meets each vertex an even number of times. n = |Q|/2 and k/n = (7-4)/7 + 2/n by Euler, giving k=38 at n=84. Regenerated from the algebra of arXiv:2610.10948 Sec. II by research/hyperbolic_psl.py; the matrices are recomputed, not copied, since that paper publishes its matrices on request only.",
  "references": [
   "arXiv:2610.10948"
  ],
  "date": "2026-10-10",
  "notes": "Distance is a homological systole: a shortest cycle in the primal graph outside the GF(2) span of the face boundaries is a genuine logical. Both the X and Z operators here are weight 3 and are carried as explicit witnesses, so d<=3 is witness-backed, not certified exact.",
  "model": "human",
  "origin": "submission",
  "search_budget": {
   "candidates_screened": 114,
   "ris_trials_per_side": 1000000
  }
 },
 "family": "topological"
}