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    218
   ],
   [
    44,
    107,
    119,
    156,
    168,
    219
   ],
   [
    45,
    108,
    120,
    157,
    169,
    220
   ],
   [
    46,
    109,
    121,
    158,
    170,
    221
   ],
   [
    47,
    110,
    122,
    159,
    171,
    222
   ],
   [
    48,
    111,
    123,
    160,
    172,
    223
   ]
  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "exact",
   "witness": [
    48,
    111
   ]
  },
  "Z": {
   "value": 2,
   "confidence": "exact",
   "witness": [
    151,
    200
   ]
  }
 },
 "family": "bivariate-bicycle",
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Periodic bivariate-bicycle code on the group algebra Z_8 x Z_14 (n = 2*l*m = 224). Convention: x = S_8 tensor I_14, y = I_8 tensor S_14 (cyclic shifts), qubit index = i*m + j; A = 1 + x^3y^9 + x^4y^7 + x^7y^2, B = 1 + x^4y^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 12783 (canonical key 4b63b4ed5740d15ebf80dcde), search lane 'w6-gap', proposal kernel 'shared-binomial-factor'. Initial NumPy lightest-logical surrogate: trials=2000, seed=1744585393. 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 3.7s, CPU time 3.4s, 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."
 }
}