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}, "Z": { "value": 28, "confidence": "upper_bound", "witness": [ 39, 82, 92, 97, 99, 118, 123, 128, 169, 181, 191, 208, 210, 219, 242, 267, 270, 276, 279, 281, 285, 290, 297, 301, 311, 313, 320, 406 ] } }, "family": "bivariate-bicycle", "provenance": { "authors": [ "@cbjuan" ], "construction": "Periodic bivariate-bicycle code on the group algebra Z_30 x Z_7 (n = 2*l*m = 420). Convention: x = S_30 tensor I_7, y = I_30 tensor S_7 (cyclic shifts), qubit index = i*m + j; A = x^2y^4 + x^8y^3 + x^10y^6, B = x^3y^1 + x^6y^3 + x^7y^5; 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 45426 (canonical key afaedf7e662d7a6f38a5e4c9), search lane 'high-distance-transfer', proposal kernel 'high-distance-correlated-step'. Initial NumPy lightest-logical surrogate: trials=8000, seed=825341658. Confirmed with an accelerated bit-packed random-information-set search at rung '1m' (1000000 trials, seed=184057557, pair_depth=16), tightest witness on side X at weight 26. An internal exact-certification attempt (same MILP method as verify/certify.py) did not close within budget on either side (side_status X=timeout, Z=timeout after 12529.7s of solver time), so this submission is a witness-backed upper bound only, not an exact claim." } }