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element x^a y^b has index a*2+b). Base matrices A = [x^2y^1, x^9, x^19y^1]; [x^1y^1, x^11, x^19] (entries act by the left regular representation L(g)[gh,h]=1) and B = [x^8y^1, x^9, x^13]; [x^17y^1, x^2y^1, x^21] (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 [[1, 1, 1], [1, 1, 1]] / [[1, 1, 1], [1, 1, 1]].", "references": [ "arXiv:2607.28795", "arXiv:2607.27644", "arXiv:2111.03654" ], "date": "2026-09-16", "notes": "Distance is a witnessed upper bound: Z side weight 9, X side weight 10, so d <= 9. Depth: screen at 300 fast RIS trials read d <= 9, ladder 10k and 100k trials read 9, 9; at packaging one fast RIS (gf2_fast) two-sided search of 300,000 trials per side (seed 7919) returned a weight-9 Z logical; a separate deep confirmation of 1,000,000 trials per side (seed 20260916) found lightest logicals of weight 10 (X) and 9 (Z) and nothing lighter (verdict corroborated). Gate refutation seed 41794491. Max check weight is 5 (2x3 monomial bases: X checks have weight 3 + 2, Z checks 2 + 3). Novelty: no [[624,52,9]] 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(24,2,13)\", \"N\": 48, \"A\": [[[5], [18], [39]], [[3], [22], [38]]], \"B\": [[[17], [18], [26]], [[35], [5], [42]]], \"w\": 5}" }, "family": "lifted-product" }