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767, 883 ], [ 480, 543, 589, 768, 880 ], [ 481, 544, 579, 769, 873 ], [ 482, 545, 584, 770, 870 ], [ 483, 546, 582, 771, 874 ], [ 484, 547, 592, 772, 879 ], [ 485, 548, 586, 773, 872 ], [ 486, 549, 594, 774, 886 ], [ 487, 550, 602, 775, 875 ], [ 488, 551, 599, 776, 892 ], [ 489, 552, 593, 777, 887 ], [ 490, 553, 598, 778, 884 ], [ 491, 554, 604, 779, 881 ], [ 492, 555, 587, 780, 885 ], [ 493, 556, 597, 781, 890 ], [ 494, 557, 596, 782, 882 ], [ 495, 558, 607, 783, 896 ], [ 496, 559, 609, 784, 888 ], [ 497, 560, 608, 785, 898 ], [ 498, 561, 605, 786, 897 ], [ 499, 562, 611, 787, 894 ], [ 500, 563, 606, 788, 891 ], [ 501, 564, 610, 789, 895 ], [ 502, 565, 603, 790, 899 ] ] }, "distance": { "d": 10, "X": { "value": 10, "confidence": "upper_bound", "witness": [ 0, 3, 40, 63, 72, 103, 112, 135, 147, 175 ] }, "Z": { "value": 10, "confidence": "upper_bound", "witness": [ 0, 3, 43, 63, 216, 219, 259, 262, 478, 495 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "Group from literal permutation generators [[[1, 21, 9], [2, 10, 22], [3, 11, 23], [4, 24, 12], [5, 17, 13], [6, 14, 18], [7, 15, 19], [8, 20, 16]], [[2, 22, 10], [4, 12, 24], [6, 18, 14], [8, 16, 20]], [[1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24]]]. Generate closure from identity by right multiplication in the listed generator order, composition a*b=a after b; index by first discovery. Source https://people.maths.bris.ac.uk/~matyd/GroupNames/61/C3%5E2s2C8.html. Left seed A=[[I,I,I],[I,L_3,L_37]], right seed B=[[I,I,I],[I,R_3,R_38]]. L_g[t,u]=1 iff u=g*t; R_h[t,u]=1 iff u=t*h. Product X(i,j) has A(i,k) on VV(k,j), B(l,j) on CC(i,l). Z(k,l) has transpose(B(l,j)) on VV(k,j), transpose(A(i,k)) on CC(i,l). Keep first independent rows in each sector.", "references": [ "https://people.maths.bris.ac.uk/~matyd/GroupNames/61/C3%5E2s2C8.html", "https://arxiv.org/abs/2111.03654", "https://arxiv.org/abs/2607.28795", "https://arxiv.org/abs/1611.07164" ], "date": "2026-10-17", "notes": "Displayed presentation: maximum check weight 5, maximum qubit degree 6, 860 checks and total incidence 4300.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }