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320, 348 ], [ 164, 191, 205, 277, 285, 321, 349 ], [ 163, 190, 206, 278, 282, 322, 350 ], [ 166, 187, 207, 279, 287, 323, 351 ], [ 165, 186, 208, 280, 284, 318, 352 ], [ 162, 189, 209, 281, 283, 319, 353 ], [ 173, 194, 210, 220, 282, 326, 354 ], [ 170, 197, 211, 219, 283, 327, 355 ], [ 169, 196, 212, 216, 284, 328, 356 ], [ 172, 193, 213, 221, 285, 329, 357 ], [ 171, 192, 214, 218, 286, 324, 358 ], [ 168, 195, 215, 217, 287, 325, 359 ] ] }, "distance": { "d": 9, "X": { "value": 10, "confidence": "upper_bound", "witness": [ 7, 15, 17, 19, 87, 91, 107, 111, 126, 134 ] }, "Z": { "value": 9, "confidence": "upper_bound", "witness": [ 73, 79, 104, 107, 113, 136, 239, 251, 263 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Lifted product over the non-abelian group algebra F_2[G], G = C12xD3 (order 72; Cayley table from research/kit/nonabelian_lp.small_nonabelian_groups). Base matrices A = [{0,6,33}, {0,44}] (entries act by the left regular representation L(g)[gh,h]=1) and B = [{0,22,47}, {0,68}] (entries act by the right regular representation R(g)[h,hg]=1). Element index lists: A = [[[0, 6, 33], [0, 44]]], B = [[[0, 22, 47], [0, 68]]]. Qubit blocks of size |G|: sector 1 holds (i,j) for i in cols(A), j in cols(B) at block i*n_B+j; sector 2 holds (r,s) for r in rows(A), s in rows(B). X-check (r,j) = [L(A[r][i]) on (i,j)] + [R(B[s][j]) on (r,s)]; Z-check (i,s) = [R(B[s][j])^T on (i,j)] + [L(A[r][i])^T on (r,s)]. Same construction as the weight-9 mitten / ZSZ-LP codes of arXiv:2607.28795 and arXiv:2607.27644 (four weight-3 entries there), here with entry weights (3,2)/(3,2), check weight 8. Built with research/kit/nonabelian_lp.lifted_product_base.", "origin": "submission", "date": "2026-09-20", "model": "Claude Fable 5.1", "notes": "Distance is a witness-backed upper bound from randomized information-set search (research/kit/surrogate.distance_rand, gf2_fast backend); screen 400 trials, ladder [9, 9, 9], packaging 200000 trials per side. Advances the unrestricted weight-8 board cell; novelty vs the literature unverified.", "search_budget": { "candidates_screened": 26210, "ris_trials_per_side": 200000, "wall_clock_hours": 1.0, "tool": "research/kit search funnel, gf2_fast RIS" } }, "family": "lifted-product" }