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 },
 "distance": {
  "d": 9,
  "X": {
   "value": 9,
   "confidence": "exact",
   "witness": [
    15,
    25,
    26,
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    118,
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   ]
  },
  "Z": {
   "value": 9,
   "confidence": "exact",
   "witness": [
    135,
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    233,
    234,
    238,
    335,
    340,
    341
   ]
  }
 },
 "family": "bivariate-bicycle",
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Periodic bivariate-bicycle code on the group algebra Z_13 x Z_15 (n = 2*l*m = 390). Convention: x = S_13 tensor I_15, y = I_13 tensor S_15 (cyclic shifts), qubit index = i*m + j; A = 1 + x^0y^11 + x^7y^2 + x^7y^8, B = 1 + x^0y^1; H_X = [A|B], H_Z = [B^T|A^T]. Found by an automated evolutionary/mutation search over (l, m, A, B) exponent sets targeting the unrestricted x weight-6 (or weight-8) board cells, screened by a randomized lightest-logical surrogate and promoted through increasing trial budgets.",
  "origin": "submission",
  "date": "2026-09-16",
  "notes": "Internal autoresearch candidate id 45064 (canonical key 62fb7cc83f4222c989d9d40d), search lane 'high-distance-transfer', proposal kernel 'exact-geometry-grid'. Initial NumPy lightest-logical surrogate: trials=8000, seed=2022249430. Confirmed with an accelerated bit-packed random-information-set search at rung '1m' (1000000 trials, seed=1618242650, pair_depth=16), tightest witness on side X at weight 9. Distance also taken through an internal exact-certification pipeline (MILP, one solve per logical-basis row per side, the same method as this repository's own verify/certify.py). Result: side_status X=exact, Z=exact (solver wall time 471625.6s, CPU time 467366.4s, summed over all per-row MILP solves on both sides). Per CONTRIBUTING.md's confidence-tier policy, this 'exact' claim is self-declared and will display as an upper bound on the board until a maintainer independently re-runs verify/certify.py and confirms it."
 }
}