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 "name": "[[64,42,4]]",
 "code_type": "CSS",
 "n": 64,
 "k": 42,
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 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
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  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
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 "provenance": {
  "authors": [
   "@MathysRennela",
   "Hirai, Yuga",
   "Suzuki, Yasunari"
  ],
  "construction": "Reproduction of the two-yoked-surface chain code check matrix q64_42_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/q64_42_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/q64_42_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=False, dominated_by=['[[64,48,4]] w=32 64-48-4.json']. 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": [
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   },
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
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    ]
   }
  },
  "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 (32 X + 32 Z CX layers per round, coloring candidate 2); 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)"
 },
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