{
 "schema_version": "0.2",
 "name": "[[54,8,6]]",
 "code_type": "CSS",
 "n": 54,
 "k": 8,
 "checks": {
  "X": [
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    0,
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    5,
    6,
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    40
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    1,
    3,
    4,
    7,
    13,
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   [
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    5,
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   [
    6,
    9,
    11,
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    18,
    46
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   [
    7,
    9,
    10,
    13,
    19,
    47
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   [
    8,
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    14,
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    45
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   [
    12,
    15,
    17,
    18,
    24,
    52
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   [
    13,
    15,
    16,
    19,
    25,
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   [
    14,
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    17,
    20,
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   [
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    21,
    23,
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    22,
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   [
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    31,
    37
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   [
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    28,
    29,
    32,
    38
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   [
    16,
    30,
    33,
    35,
    36,
    42
   ],
   [
    17,
    31,
    33,
    34,
    37,
    43
   ],
   [
    15,
    32,
    34,
    35,
    38,
    44
   ],
   [
    22,
    36,
    39,
    41,
    42,
    48
   ],
   [
    23,
    37,
    39,
    40,
    43,
    49
   ],
   [
    21,
    38,
    40,
    41,
    44,
    50
   ],
   [
    0,
    28,
    42,
    45,
    47,
    48
   ],
   [
    0,
    6,
    34,
    48,
    51,
    53
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  ],
  "Z": [
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    0,
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    3,
    20,
    45,
    51
   ],
   [
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    18,
    46,
    52
   ],
   [
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    5,
    19,
    47,
    53
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   [
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    7,
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   [
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    8,
    10,
    24,
    52
   ],
   [
    5,
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    8,
    11,
    25,
    53
   ],
   [
    3,
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    12,
    13,
    15,
    32
   ],
   [
    4,
    10,
    13,
    14,
    16,
    30
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   [
    5,
    11,
    12,
    14,
    17,
    31
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   [
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    19,
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   [
    10,
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    19,
    20,
    22,
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   [
    11,
    17,
    18,
    20,
    23,
    37
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   [
    15,
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    24,
    25,
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   ],
   [
    16,
    22,
    25,
    26,
    28,
    42
   ],
   [
    21,
    27,
    30,
    31,
    33,
    50
   ],
   [
    22,
    28,
    31,
    32,
    34,
    48
   ],
   [
    23,
    29,
    30,
    32,
    35,
    49
   ],
   [
    2,
    27,
    33,
    36,
    37,
    39
   ],
   [
    0,
    28,
    34,
    37,
    38,
    40
   ],
   [
    1,
    29,
    35,
    36,
    38,
    41
   ],
   [
    8,
    33,
    39,
    42,
    43,
    45
   ],
   [
    7,
    35,
    41,
    42,
    44,
    47
   ],
   [
    14,
    39,
    45,
    48,
    49,
    51
   ]
  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    12,
    13,
    16,
    22,
    31,
    50
   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    8,
    14,
    15,
    16,
    35,
    52
   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Reconstructed from qecdb.org record (see provenance.references); H-field X/Z row split, k recomputed, witnesses from the kit's random search.",
  "origin": "submission",
  "date": "2026-08-15",
  "model": "DeepSeek V4 Flash 0731"
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "X": {
    "value": 6,
    "confidence": "upper_bound",
    "witness": [
     48,
     49,
     112,
     113,
     132,
     250
    ]
   },
   "Z": {
    "value": 6,
    "confidence": "upper_bound",
    "witness": [
     604,
     618,
     727,
     815,
     930,
     1212
    ]
   }
  },
  "rounds": 6,
  "stim_version": "1.16.0",
  "notes": "Flag-qubit sequential two-block extraction: one ancilla and one flag qubit per check, X checks then Z checks each round with joint reset/measure layers. Each check's 6 CNOTs occupy 6 slot layers (a proper edge coloring of its Tanner graph); the flag (|0> for X checks, |+> for Z checks) is coupled to the ancilla after the check's CNOT 1 and again after CNOT 5, and measured every round as a single-record detector, so an ancilla hook in that window also fires the flag. 8 X + 8 Z CX layers per round, schedule seed 0. Hook-aware orders: every proper suffix S_j of a check's CNOT order needs >= d-1 further data errors if unflagged and >= d-2 if flagged, and every same-ancilla pair of hooks needs >= d-2 (or d-3 when exactly one is flagged) further errors to complete a logical; layered by min-conflicts search. Screened by RIS on ker(H_dem) and an observable-constrained seeded BP+OSD search; witnesses validated in GF(2).",
  "contributed_by": {
   "by": [
    "@vprusso"
   ],
   "date": "2026-09-19",
   "method": "generic CSS memory schedule with one flag qubit per check: CX layers from a bipartite edge coloring, the flag coupled to the ancilla after the first and the fifth CNOT and measured every round, CNOT orders filtered by a single- and pair-hook cost criterion; screened by RIS on ker(H_dem) and an observable-constrained seeded BP+OSD search"
  }
 },
 "locality": {
  "coordinates": [
   [
    4,
    5
   ],
   [
    5,
    3
   ],
   [
    3,
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   ],
   [
    5,
    4
   ],
   [
    5,
    6
   ],
   [
    4,
    6
   ],
   [
    5,
    7
   ],
   [
    7,
    5
   ],
   [
    2,
    7
   ],
   [
    7,
    4
   ],
   [
    5,
    5
   ],
   [
    2,
    5
   ],
   [
    4,
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   ],
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    6,
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   ],
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   ],
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    3,
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   ],
   [
    6,
    2
   ],
   [
    5,
    2
   ],
   [
    1,
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   ],
   [
    5,
    1
   ],
   [
    1,
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   ],
   [
    1,
    3
   ],
   [
    6,
    4
   ],
   [
    3,
    4
   ],
   [
    2,
    3
   ],
   [
    3,
    1
   ],
   [
    2,
    2
   ],
   [
    3,
    0
   ],
   [
    3,
    2
   ],
   [
    0,
    3
   ],
   [
    4,
    2
   ],
   [
    0,
    2
   ],
   [
    4,
    3
   ],
   [
    4,
    1
   ],
   [
    2,
    1
   ],
   [
    1,
    1
   ],
   [
    6,
    1
   ],
   [
    1,
    5
   ],
   [
    4,
    4
   ],
   [
    6,
    3
   ],
   [
    3,
    3
   ],
   [
    0,
    5
   ],
   [
    7,
    2
   ],
   [
    1,
    6
   ],
   [
    7,
    7
   ],
   [
    6,
    5
   ],
   [
    2,
    6
   ],
   [
    0,
    4
   ],
   [
    4,
    0
   ],
   [
    3,
    7
   ],
   [
    7,
    6
   ],
   [
    6,
    7
   ]
  ],
  "layers": 1,
  "contributed_by": {
   "by": [
    "@mathysrennela"
   ],
   "date": "2026-09-19",
   "method": "simulated annealing over integer grid sites (research/local2d/fold_layout.py)"
  }
 }
}