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Base matrices A = [{0,13,51}, {0,44}] (entries act by the left regular representation L(g)[gh,h]=1) and B = [{0,41,61}, {0,8}] (entries act by the right regular representation R(g)[h,hg]=1). Element index lists: A = [[[0, 13, 51], [0, 44]]], B = [[[0, 41, 61], [0, 8]]]. 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 [10, 10, 10], 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" }