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 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "exact",
   "witness": [
    57,
    87,
    99
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "exact",
   "witness": [
    67,
    79,
    91
   ]
  }
 },
 "family": "bivariate-bicycle",
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Periodic bivariate-bicycle code on the group algebra Z_3 x Z_18 (n = 2*l*m = 108). Convention: x = S_3 tensor I_18, y = I_3 tensor S_18 (cyclic shifts), qubit index = i*m + j; A = 1 + x^0y^7 + x^0y^12 + x^1y^1 + x^1y^2 + x^1y^6 + x^2y^6 + x^2y^14, B = 1 + x^0y^12 + x^0y^15 + x^1y^13 + x^2y^0 + x^2y^3 + x^2y^6 + x^2y^7; 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 2359 (canonical key 0daec5be0e4e5f579efebaee), search lane 'breadth', proposal kernel 'shared-binomial-factor'. Initial NumPy lightest-logical surrogate: trials=2000, seed=1571305854. 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 16.4s, CPU time 15.8s, 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."
 }
}