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  ]
 },
 "distance": {
  "d": 9,
  "X": {
   "value": 9,
   "confidence": "exact",
   "witness": [
    96,
    100,
    101,
    128,
    129,
    134,
    259,
    263,
    269
   ]
  },
  "Z": {
   "value": 9,
   "confidence": "exact",
   "witness": [
    122,
    128,
    133,
    156,
    160,
    161,
    262,
    263,
    268
   ]
  }
 },
 "family": "bivariate-bicycle",
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Periodic bivariate-bicycle code on the group algebra Z_9 x Z_15 (n = 2*l*m = 270). Convention: x = S_9 tensor I_15, y = I_9 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 10524 (canonical key 88d55b4bd0c3fcfa2b2856da), search lane 'w6-gap', proposal kernel 'hybrid'. Initial NumPy lightest-logical surrogate: trials=8000, seed=852276647. Confirmed with an accelerated bit-packed random-information-set search at rung '60k' (60000 trials, seed=852276664, 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 34662.8s, CPU time 34240.1s, 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."
 }
}