{
 "schema_version": "0.2",
 "name": "[[36,16,4]]",
 "code_type": "CSS",
 "n": 36,
 "k": 16,
 "checks": {
  "X": [
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    0,
    1,
    2,
    3,
    4,
    5
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   [
    6,
    7,
    8,
    9,
    10,
    11
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   [
    12,
    13,
    14,
    15,
    16,
    17
   ],
   [
    18,
    19,
    20,
    21,
    22,
    23
   ],
   [
    24,
    25,
    26,
    27,
    28,
    29
   ],
   [
    30,
    31,
    32,
    33,
    34,
    35
   ],
   [
    0,
    1,
    6,
    7,
    12,
    13,
    18,
    19,
    24,
    25,
    30,
    31
   ],
   [
    0,
    2,
    6,
    8,
    12,
    14,
    18,
    20,
    24,
    26,
    30,
    32
   ],
   [
    0,
    3,
    6,
    9,
    12,
    15,
    18,
    21,
    24,
    27,
    30,
    33
   ],
   [
    0,
    4,
    6,
    10,
    12,
    16,
    18,
    22,
    24,
    28,
    30,
    34
   ]
  ],
  "Z": [
   [
    0,
    1,
    2,
    3,
    4,
    5
   ],
   [
    6,
    7,
    8,
    9,
    10,
    11
   ],
   [
    12,
    13,
    14,
    15,
    16,
    17
   ],
   [
    18,
    19,
    20,
    21,
    22,
    23
   ],
   [
    24,
    25,
    26,
    27,
    28,
    29
   ],
   [
    30,
    31,
    32,
    33,
    34,
    35
   ],
   [
    1,
    5,
    7,
    11,
    13,
    17,
    19,
    23,
    25,
    29,
    31,
    35
   ],
   [
    2,
    5,
    8,
    11,
    14,
    17,
    20,
    23,
    26,
    29,
    32,
    35
   ],
   [
    3,
    5,
    9,
    11,
    15,
    17,
    21,
    23,
    27,
    29,
    33,
    35
   ],
   [
    4,
    5,
    10,
    11,
    16,
    17,
    22,
    23,
    28,
    29,
    34,
    35
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    25,
    27,
    31,
    33
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    25,
    27,
    31,
    33
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela",
   "Hirai, Yuga",
   "Suzuki, Yasunari"
  ],
  "construction": "Reproduction of the two-yoked-surface chain code check matrix q36_16_4.txt of Hirai and Suzuki (arXiv:2610.04613 Sec. IV.1-IV.3), taken from github.com/yugahirai/multi_yoked_surface_codes @ b3e8b3e, `ecc/chain_codes/2_yoke/q36_16_4.txt`, used verbatim: the published max check weight already sits at the board cap, so nothing was changed. Re-derived here and re-verified (CSS commutation, k, and the distance witness) rather than copied from the paper's table.",
  "origin": "submission",
  "date": "2026-10-06",
  "model": "MiMo-V2.6-Flash",
  "references": [
   "arXiv:2610.04613"
  ],
  "novelty": "known_parameters",
  "notes": "Reproduction of the published matrix, not a new construction: the checks come from github.com/yugahirai/multi_yoked_surface_codes @ b3e8b3e, `ecc/chain_codes/2_yoke/q36_16_4.txt`, unchanged for the two-yoke entries and re-generated as an equivalent basis of the same row space for the three-yoke ones. Checked against the current board by exact fingerprint and WL signature with local-Hadamard images included: exact_duplicate_of=None, wl_equivalent_of=None, board_advancing=True, dominated_by=[]. qldpc submit runs its own dedup pass after writing this file, so the draft body first matched the candidate against itself; the verdict above was taken with the file off the board. Literature novelty: known_parameters -- the parameter set is published in arXiv:2610.04613."
 },
 "family": "other",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     2578,
     2579
    ]
   },
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     1691,
     1692
    ]
   }
  },
  "rounds": 4,
  "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 (13 X + 12 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)"
 },
 "locality": {
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  "layers": 2,
  "interaction_radius": 4.1232,
  "contributed_by": {
   "by": [
    "@dorakingx"
   ],
   "date": "2026-10-07",
   "method": "Simulated annealing over site assignments on an integer grid with the repo's own research/local2d/fold_layout.search_layout (max-diameter objective, several bounding boxes and seeds); single layer at radius 4 tried first, then two layers at 7. Radius and per-site occupancy re-measured with the verifier's rule."
  }
 }
}