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676, 681, 768, 774, 821, 872, 892, 970 ], [ 654, 677, 722, 775, 839, 873, 921, 971 ], [ 672, 678, 742, 776, 796, 874, 906, 972 ], [ 655, 679, 723, 777, 788, 875, 905, 973 ], [ 670, 680, 740, 778, 795, 876, 893, 974 ], [ 657, 681, 725, 779, 808, 877, 894, 975 ], [ 680, 682, 755, 780, 806, 878, 920, 976 ], [ 666, 683, 737, 781, 794, 879, 919, 977 ], [ 678, 684, 753, 782, 805, 880, 903, 978 ] ] }, "distance": { "d": 6, "X": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 4, 6, 63, 127, 161 ] }, "Z": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 4, 6, 22, 299, 316 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "Literal primary GroupNames permutation source is recorded in group_source.json, with original cycles and primary URL. Identity-first breadth-first group enumeration appends x*g for each listed generator in order; permutation composition (x*g)[i]=x[g[i]]. Full multiplication table follows this discovery ordering. Group order 98. L_g[t,u]=1 iff u=g*t; R_h[t,u]=1 iff u=t*h. A=[I+L6,I+L24,I+L56]; B=[I+R6,I+R24,I+R72], binary sums. Nine VV(k,j) blocks indexed 3*k+j precede one CC block, each size 98. X(j) has A(k) on VV(k,j) and B(j) on CC. Z(k) has B(j)^T on VV(k,j) and A(k)^T on CC. Keep first independent original rows, 291 per sector.", "references": [ "https://arxiv.org/abs/2111.03654", "https://arxiv.org/abs/2607.28795" ], "date": "2026-10-17", "notes": "Displayed presentation: maximum check weight 8, maximum qubit degree 12, 582 checks and total incidence 4656.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }