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532, 540, 632, 635 ], [ 310, 311, 533, 541, 633, 636 ], [ 311, 312, 534, 542, 634, 637 ], [ 312, 313, 535, 543, 635, 638 ], [ 313, 314, 536, 544, 636, 639 ], [ 314, 315, 537, 545, 637, 640 ], [ 315, 316, 532, 538, 638, 641 ], [ 316, 317, 533, 539, 639, 642 ], [ 317, 318, 534, 540, 640, 643 ], [ 318, 319, 535, 541, 630, 641 ], [ 319, 320, 536, 542, 631, 642 ], [ 320, 321, 537, 543, 632, 643 ] ] }, "distance": { "d": 8, "X": { "value": 8, "confidence": "exact", "witness": [ 57, 160, 163, 380, 382, 385, 388, 391 ] }, "Z": { "value": 8, "confidence": "exact", "witness": [ 84, 86, 89, 92, 95, 409, 639, 642 ] } }, "family": "bivariate-bicycle", "provenance": { "authors": [ "@cbjuan" ], "construction": "Periodic bivariate-bicycle code on the group algebra Z_23 x Z_14 (n = 2*l*m = 644). Convention: x = S_23 tensor I_14, y = I_23 tensor S_14 (cyclic shifts), qubit index = i*m + j; A = 1 + x^0y^11 + x^7y^2 + x^7y^8, B = 1 + x^0y^1; 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 45043 (canonical key bd31490bf37075eeec2ed5c5), search lane 'high-distance-transfer', proposal kernel 'exact-geometry-grid'. Initial NumPy lightest-logical surrogate: trials=8000, seed=1672093543. Confirmed with an accelerated bit-packed random-information-set search at rung '1m' (1000000 trials, seed=128654387, pair_depth=16), tightest witness on side X at weight 8. 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 36749.8s, CPU time 36230.2s, 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." } }