{
 "schema_version": "0.2",
 "name": "[[53,20,3]]",
 "code_type": "CSS",
 "n": 53,
 "k": 20,
 "checks": {
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    3,
    7,
    16,
    32,
    35,
    41
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    13,
    20,
    41,
    49,
    50
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    28,
    44,
    46,
    51
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   [
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    44,
    45
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   [
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    34,
    38,
    39,
    43
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   [
    12,
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    21,
    24,
    26,
    31
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   [
    1,
    5,
    8,
    14,
    18,
    28
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   [
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    2,
    10,
    25,
    26
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    30,
    33,
    35,
    40
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   [
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    4,
    14,
    17,
    33,
    36
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    52
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    24,
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    48,
    50
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   [
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    11,
    27,
    43,
    48
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    45,
    49
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    25,
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    51,
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    29,
    34,
    37,
    46
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   [
    15,
    18,
    19,
    29,
    31,
    40
   ]
  ],
  "Z": [
   [
    1,
    2,
    16,
    18,
    29,
    32
   ],
   [
    3,
    10,
    15,
    19,
    25,
    41
   ],
   [
    11,
    12,
    21,
    23,
    30,
    43
   ],
   [
    5,
    11,
    15,
    18,
    27,
    45
   ],
   [
    16,
    21,
    24,
    41,
    46,
    50
   ],
   [
    2,
    25,
    30,
    33,
    36,
    39
   ],
   [
    5,
    28,
    34,
    39,
    46,
    47
   ],
   [
    4,
    10,
    17,
    20,
    26,
    34
   ],
   [
    4,
    8,
    14,
    22,
    37,
    42
   ],
   [
    6,
    19,
    22,
    40,
    47,
    52
   ],
   [
    13,
    20,
    38,
    44,
    51,
    52
   ],
   [
    9,
    23,
    32,
    35,
    42,
    51
   ],
   [
    3,
    7,
    8,
    28,
    44,
    48
   ],
   [
    6,
    17,
    24,
    27,
    33,
    48
   ],
   [
    0,
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    36,
    45,
    49,
    50
   ],
   [
    12,
    13,
    29,
    31,
    37,
    49
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    4,
    14,
    26
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    12,
    13,
    24,
    50
   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Check deletion and degree-one r=1 removal from board [[54,20,4]]: drop qubit 19 plus one Z stabilizer; found and reconstructed by MiMo-V2.6-Flash.",
  "origin": "submission",
  "date": "2026-09-26",
  "model": "MiMo-V2.6-Flash",
  "notes": "Found and reconstructed by MiMo-V2.6-Flash."
 },
 "locality": {
  "coordinates": [
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    5.0,
    9.0
   ],
   [
    7.0,
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   [
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   [
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   [
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   [
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   [
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   ],
   [
    8.0,
    6.0
   ],
   [
    10.0,
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  ],
  "layers": 2
 },
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     742,
     775
    ]
   },
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     1854,
     1855
    ]
   }
  },
  "rounds": 3,
  "stim_version": "1.16.0",
  "notes": "Generic sequential two-block extraction: one ancilla per check, X checks then Z checks each round with joint reset and measurement layers; CX layers are a proper edge coloring of each Tanner graph (7 X + 7 Z CX layers per round, coloring candidate 0); generated by qldpc submit (research/circuit_autogen.py, seed 0), the first of up to 6 candidates whose RIS screen at 2 rounds found nothing below d; witnesses from RIS on ker(H_dem) at twice the gate's trial budget, validated in GF(2)"
 }
}