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239, 275, 345, 349 ], [ 182, 193, 206, 212, 276, 280, 346 ], [ 141, 150, 207, 241, 277, 281, 347 ], [ 184, 195, 208, 214, 278, 282, 348 ], [ 143, 152, 209, 243, 279, 283, 349 ] ] }, "distance": { "d": 9, "X": { "value": 9, "confidence": "upper_bound", "witness": [ 143, 155, 168, 179, 189, 202, 213, 255, 279 ] }, "Z": { "value": 9, "confidence": "upper_bound", "witness": [ 18, 22, 39, 60, 63, 64, 148, 186, 200 ] } }, "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "model": "Claude Fable 5.1 (Claude Code)", "construction": "Lifted product over the non-abelian group algebra F_2[G], G = Z_35 x|_29 Z_2 (order 70; generators x, y with x^35 = y^2 = 1, y x = x^29 y; element x^a y^b has index a*2+b). Base matrices A = [1 + x^14 + x^15y^1, 1 + x^2] (entries act by the left regular representation L(g)[gh,h]=1) and B = [1 + x^12 + x^28y^1, 1 + x^32] (entries act by the right regular representation R(g)[h,hg]=1). 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 (which are the case of four weight-3 entries), here with entry weights [[3, 2]] / [[3, 2]].", "references": [ "arXiv:2607.28795", "arXiv:2607.27644", "arXiv:2111.03654" ], "date": "2026-09-16", "notes": "Distance is a witnessed upper bound (both sides weight 9). Depth: screen at 300 fast RIS trials read d <= 9, ladder 10k and 100k trials read 9, 9; at packaging two independent fast RIS (gf2_fast) two-sided searches of 1,000,000 trials per side (seeds 7919 and 15838) each returned a weight-9 X logical and nothing lighter on either side. Gate refutation seed 1065517832. Novelty: no [[350,70,9]] and no isomorphic code found in the 2BGA, GB, BB, QECDB and codetables data (Tanner-graph canonical-form check with pynauty); parameters claimed new, not verifier-proved. Not equivalent to a board entry (validator dedup found no exact or WL-equivalent match). Sampler spec: {\"family\": \"nonabelian-lp\", \"group\": \"ZSZ(35,2,29)\", \"N\": 70, \"A\": [[[0, 28, 31], [0, 4]]], \"B\": [[[0, 24, 57], [0, 64]]], \"w\": 8}" }, "family": "lifted-product" }