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366, 436, 524 ], [ 259, 334, 367, 437, 525 ], [ 260, 335, 368, 432, 526 ], [ 261, 330, 369, 433, 527 ], [ 262, 331, 370, 434, 522 ], [ 263, 332, 371, 435, 523 ], [ 264, 297, 372, 442, 530 ], [ 265, 298, 373, 443, 531 ], [ 266, 299, 374, 438, 532 ], [ 267, 294, 375, 439, 533 ], [ 268, 295, 376, 440, 528 ], [ 269, 296, 377, 441, 529 ] ] }, "distance": { "d": 8, "X": { "value": 8, "confidence": "upper_bound", "witness": [ 149, 156, 172, 189, 197, 215, 230, 247 ] }, "Z": { "value": 8, "confidence": "upper_bound", "witness": [ 64, 79, 173, 189, 199, 319, 324, 335 ] } }, "provenance": { "authors": [ "@msilve160" ], "construction": "Lifted product of two 2x3 monomial base matrices A, B over F_2[G], G = C_7 x D_3 (direct product, order 42) (|G|=42), 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" }