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  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "exact",
   "witness": [
    47,
    126,
    182
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "exact",
   "witness": [
    8,
    48,
    103
   ]
  }
 },
 "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^2y^9 + x^5y^4 + x^6y^5, B = 1 + x^6y^5; 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 11462 (canonical key 508dfbd86da7054d628fa1eb), search lane 'w6-gap', proposal kernel 'shared-binomial-factor'. Initial NumPy lightest-logical surrogate: trials=8000, seed=2136219389. Confirmed with an accelerated bit-packed random-information-set search at rung '60k' (60000 trials, seed=2136219406, pair_depth=16), tightest witness on side X at weight 3. 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 459.7s, CPU time 452.8s, 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."
 }
}