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103, 107, 124, 167, 175 ] }, "Z": { "value": 10, "confidence": "upper_bound", "witness": [ 0, 3, 9, 15, 192, 195, 207, 209, 393, 401 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "Group from literal permutation generators [[[1, 9], [2, 20], [3, 11], [4, 22], [5, 13], [6, 24], [7, 15], [8, 26], [10, 28], [12, 30], [14, 32], [16, 18], [17, 25], [19, 27], [21, 29], [23, 31]], [[1, 27], [2, 28], [3, 29], [4, 30], [5, 31], [6, 32], [7, 17], [8, 18], [9, 19], [10, 20], [11, 21], [12, 22], [13, 23], [14, 24], [15, 25], [16, 26]], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]]]. 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/C2%5E2sC16.html. Left seed A=[[I,I,I],[I,L_3,L_13]], right seed B=[[I,I,I],[I,R_3,R_25]]. 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/C2%5E2sC16.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, 764 checks and total incidence 3820.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }