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111, 343, 458, 459, 690, 691 ], [ 112, 344, 459, 460, 691, 692 ], [ 113, 345, 460, 461, 692, 693 ], [ 114, 346, 461, 462, 693, 694 ], [ 115, 347, 462, 463, 694, 695 ] ] }, "distance": { "d": 3, "X": { "value": 3, "confidence": "exact", "witness": [ 60, 176, 292 ] }, "Z": { "value": 3, "confidence": "exact", "witness": [ 68, 184, 300 ] } }, "family": "bivariate-bicycle", "provenance": { "authors": [ "@cbjuan" ], "construction": "Periodic bivariate-bicycle code on the group algebra Z_3 x Z_116 (n = 2*l*m = 696). Convention: x = S_3 tensor I_116, y = I_3 tensor S_116 (cyclic shifts), qubit index = i*m + j; A = 1 + x^0y^1 + x^2y^0 + x^2y^1, B = 1 + x^2y^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 40001 (canonical key 81f0c752c6a53caf224d8ce8), search lane 'factor-order-continuation', proposal kernel 'explicit-transfer'. Initial NumPy lightest-logical surrogate: trials=8000, seed=2031276414. Confirmed with an accelerated bit-packed random-information-set search at rung '1m' (1000000 trials, seed=2031276431, 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 4767.6s, CPU time 4708.7s, 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." } }