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282, 501, 540, 571 ], [ 238, 262, 283, 502, 541, 572 ], [ 239, 263, 284, 503, 542, 573 ] ] }, "distance": { "d": 30, "X": { "value": 30, "confidence": "upper_bound", "witness": [ 19, 40, 64, 105, 109, 126, 130, 139, 147, 154, 160, 171, 184, 208, 262, 324, 428, 435, 439, 440, 457, 466, 471, 498, 502, 505, 510, 542, 568, 573 ] }, "Z": { "value": 32, "confidence": "upper_bound", "witness": [ 10, 22, 29, 30, 41, 42, 75, 81, 87, 93, 100, 112, 126, 138, 145, 146, 157, 158, 177, 189, 197, 209, 247, 259, 267, 279, 339, 351, 410, 422, 467, 479 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 300000000, "survived_samples": 300000000, "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)", "seeds": [ 4101 ] } } }, "family": "bivariate-bicycle", "provenance": { "authors": [ "@cbjuan" ], "construction": "Periodic bivariate-bicycle code on the group algebra Z_12 x Z_24 (n = 2*l*m = 576). Convention: x = S_12 tensor I_24, y = I_12 tensor S_24 (cyclic shifts), qubit index = i*m + j; A = x^0y^2 + x^1y^9 + x^3y^0, B = x^0y^3 + x^1y^0 + 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 56213 (canonical key d2e5e445f5073e9e2650558f), search lane 'refreshed-high-distance-mutation', proposal kernel 'validated-highd-two-step'. Initial NumPy lightest-logical surrogate: trials=8000, seed=872600066. Confirmed with an accelerated bit-packed random-information-set search at rung '1m' (1000000 trials, seed=843120991, pair_depth=16), tightest witness on side X at weight 30. 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 340847.3s of solver time), so this submission is a witness-backed upper bound only, not an exact claim." } }