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{ "value": 12, "confidence": "upper_bound", "witness": [ 2, 3, 10, 11, 18, 19, 78, 79, 86, 87, 94, 95 ] }, "Z": { "value": 14, "confidence": "upper_bound", "witness": [ 43, 48, 52, 62, 231, 240, 250, 260, 392, 402, 434, 444, 538, 580 ] } }, "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 (R3EliteP02, 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 [[1500,76,<=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 (R3EliteP02 at t=30, reported [[1500,76,<=20]]); 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" }