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    673,
    676,
    688,
    691
   ],
   [
    341,
    344,
    607,
    610,
    674,
    677,
    689,
    692
   ],
   [
    342,
    345,
    608,
    611,
    675,
    678,
    690,
    693
   ],
   [
    343,
    346,
    600,
    609,
    676,
    679,
    691,
    694
   ],
   [
    344,
    347,
    601,
    610,
    677,
    680,
    692,
    695
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "exact",
   "witness": [
    241,
    256,
    335,
    589
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "exact",
   "witness": [
    318,
    584,
    651,
    666
   ]
  }
 },
 "family": "bivariate-bicycle",
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Periodic bivariate-bicycle code on the group algebra Z_29 x Z_12 (n = 2*l*m = 696). Convention: x = S_29 tensor I_12, y = I_29 tensor S_12 (cyclic shifts), qubit index = i*m + j; A = 1 + x^0y^3 + x^1y^3 + x^1y^6 + x^7y^1 + x^7y^10, B = 1 + x^0y^3; 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 40005 (canonical key b68a3301fb2cf7ca72c47e01), search lane 'factor-order-continuation', proposal kernel 'explicit-transfer'. Initial NumPy lightest-logical surrogate: trials=8000, seed=1188030041. Confirmed with an accelerated bit-packed random-information-set search at rung '1m' (1000000 trials, seed=120306883, pair_depth=16), tightest witness on side X at weight 4. 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 28911.2s, CPU time 28671.4s, 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."
 }
}