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"confidence": "exact", "witness": [ 64, 176, 288 ] } }, "family": "bivariate-bicycle", "provenance": { "authors": [ "@cbjuan" ], "construction": "Periodic bivariate-bicycle code on the group algebra Z_21 x Z_16 (n = 2*l*m = 672). Convention: x = S_21 tensor I_16, y = I_21 tensor S_16 (cyclic shifts), qubit index = i*m + j; A = x^1y^9 + x^4y^0 + x^8y^9 + x^11y^0, B = x^1y^12 + x^4y^0 + x^8y^12 + x^11y^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 40004 (canonical key 6483270b1443581219aa61b1), search lane 'factor-order-continuation', proposal kernel 'explicit-transfer'. Initial NumPy lightest-logical surrogate: trials=8000, seed=978692489. Confirmed with an accelerated bit-packed random-information-set search at rung '1m' (1000000 trials, seed=249566305, 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 40950.3s, CPU time 40544.9s, 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." } }