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  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "exact",
   "witness": [
    16,
    47,
    78,
    109
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "exact",
   "witness": [
    135,
    166,
    197,
    228
   ]
  }
 },
 "family": "bivariate-bicycle",
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Periodic bivariate-bicycle code on the group algebra Z_4 x Z_31 (n = 2*l*m = 248). Convention: x = S_4 tensor I_31, y = I_4 tensor S_31 (cyclic shifts), qubit index = i*m + j; A = 1 + x^0y^30 + x^2y^0 + x^3y^30, B = 1 + x^1y^0; 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 19531 (canonical key 4fba9c6576927c998ae3a408), search lane 'w6-gap', proposal kernel 'hybrid'. Initial NumPy lightest-logical surrogate: trials=8000, seed=172055528. 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 20.2s, CPU time 19.5s, 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."
 }
}