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"value": 8, "confidence": "upper_bound", "witness": [ 52, 53, 64, 65, 80, 81, 92, 93 ] }, "Z": { "value": 12, "confidence": "upper_bound", "witness": [ 73, 75, 79, 83, 87, 175, 189, 277, 363, 365, 377, 383 ] } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Lifted product over Z_t x Z_2 (|G|=24), protograph A (3x4), B (3x4) taken from arXiv:2606.24808 Table 1 (R3EliteP01, an SCE search elite), with the paper's exponents reduced modulo the family parameter t=12 to fit the board's n<=700 cap (n = (nA*nB + mA*mB)*|G| = 25*24 = 600). Entries of A act by left regular representation, entries of B by right regular representation (via inverse), HX = [A~(x)I | I(x)B~^T], HZ = [I(x)B~^T-blocks | A~^T-blocks]. Paper reports [[1500,81,<=pd]] at t=30; this is the same protograph at a smaller lift. Distance is an upper bound from the kit's randomized witness search.", "references": [ "arXiv:2606.24808" ], "date": "2026-09-14", "notes": "Construction family and protograph published in arXiv:2606.24808 (R3EliteP01 at t=30, reported [[1500,81,<=18]]); this entry is the same protograph at a new, smaller lift (t=12), a parameter point the paper does not tabulate; literature novelty of the parameter set unverified. Board dedup gate-checked: not an exact or WL-equivalent duplicate of any existing entry.", "model": "GLM 5.3 Flash", "origin": "submission" }, "family": "lifted-product" }