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], [ 280, 322, 329, 378, 470, 500, 560, 586, 626 ], [ 282, 331, 351, 386, 472, 501, 513, 534, 627 ], [ 288, 330, 354, 384, 491, 502, 568, 576, 628 ], [ 297, 339, 346, 381, 485, 503, 577, 602, 629 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 281, 289, 299, 332, 335, 348, 383, 393, 414, 430, 432, 434, 438, 454, 458, 461, 463, 471, 487, 489 ] }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 5, 10, 31, 35, 41, 50, 82, 87, 93, 254, 290, 291, 315, 325, 333, 347, 353, 358, 359, 364 ] } }, "provenance": { "authors": [ "Bhardwaj, Aditya", "Ma, Muzhou", "Meister, Nadine", "King, Robbie", "Bluvstein, Dolev", "Preskill, John", "Cain, Madelyn", "Xu, Qian", "Huang, Hsin-Yuan" ], "construction": "Mitten code (arXiv:2607.28795, Definition 4): lifted product LP(A,B) over F2[G], G = GAP SmallGroup(126,1) = C7 : C18, base matrices A = [a0|a1], B = [b0|b1] from Table XIII, entries as 0-based indices into Elements(G): a0=[50, 117, 123], a1=[0, 62, 104], b0=[4, 39, 82], b1=[0, 67, 87]. Block form H_X = [[L(a0),0,L(a1),0,R(b0*)],[0,L(a0),0,L(a1),R(b1*)]], H_Z = [[R(b0),R(b1),0,0,L(a0*)],[0,0,R(b0),R(b1),L(a1*)]] with L(g)b(h)=b(gh), R(g)b(h)=b(h g^-1) and * the g->g^-1 involution (paper Definition 8). Check matrices taken from the authors' repository (github.com/a7b/yarn @ 82fb695a1e40, processor_codes/mitten). Independent reconstruction from Table XIII + GAP Elements ordering reproduces the published H_X/H_Z bit-for-bit.", "references": [ "arXiv:2607.28795" ], "date": "2026", "notes": "Literature baseline. Paper claims d = 20 (upper bound estimate from >50M sQetch + >50k BP+OSD iterations). Seeded per issue #377.", "origin": "baseline" }, "family": "lifted-product" }