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F_2[G], G = Z_5 x|_4 Z_8 (metacyclic, relation y x = x^4 y) (|G|=40), entries acting by the left (A) and right (B) regular representation (research/kit/nonabelian_lp.py, lifted_product_base). n = 13|G|, check weight 5 (row weight 3 of A + row weight 2 of B, and vice versa). Same construction family as arXiv:2607.28795 (mitten codes) / arXiv:2607.27644 (ZSZ lifted products), at lower entry weight (monomial, not trinomial) than the published weight-9 form. Reproduces a candidate flagged but not submitted in fieldnotes/2026-09-16-lifted-product-girth-cap.md (Finding 5), found via the merged research/kit/nonabelian_lp.sample_nonabelian_lp sampler. This gap in the check-weight-5 region of the board was found by @vprusso (using Claude Fable 5.1), who also wrote research/kit/nonabelian_lp.py and submitted the neighboring codes/624-52-9.json from the same campaign; see fieldnotes/2026-09-16-lifted-product-girth-cap.md for the original search (this submission reproduces one of that campaign's flagged-but-unsubmitted points using the already-merged tooling).", "references": [ "arXiv:2607.28795", "arXiv:2607.27644" ], "date": "2026-09-19", "notes": "", "model": "Claude Sonnet 5" }, "family": "lifted-product" }