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"confidence": "exact", "witness": [ 26, 82, 138 ] }, "Z": { "value": 3, "confidence": "exact", "witness": [ 20, 52, 108 ] } }, "family": "bivariate-bicycle", "provenance": { "authors": [ "@cbjuan" ], "construction": "Periodic bivariate-bicycle code on the group algebra Z_6 x Z_24 (n = 2*l*m = 288). Convention: x = S_6 tensor I_24, y = I_6 tensor S_24 (cyclic shifts), qubit index = i*m + j; A = 1 + x^1y^2 + x^2y^8 + x^3y^10, B = 1 + x^0y^9 + x^2y^8 + x^2y^17; 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 16394 (canonical key ec8a86c6f4ad6ca4ee96039a), search lane 'w8-gap', proposal kernel 'shared-binomial-factor'. Initial NumPy lightest-logical surrogate: trials=8000, seed=1804300979. Confirmed with an accelerated bit-packed random-information-set search at rung '60k' (60000 trials, seed=1804300996, 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 491.0s, CPU time 483.8s, 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." } }