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655, 739, 746, 790, 823 ], [ 535, 572, 656, 667, 715, 740, 824, 828 ], [ 557, 573, 650, 657, 733, 741, 770, 825 ], [ 574, 577, 651, 658, 742, 754, 791, 826 ], [ 560, 575, 652, 659, 735, 743, 808, 827 ], [ 543, 576, 654, 660, 720, 744, 765, 828 ], [ 545, 577, 661, 668, 722, 745, 777, 829 ], [ 555, 578, 606, 662, 682, 746, 769, 830 ], [ 579, 584, 607, 663, 708, 747, 806, 831 ], [ 551, 580, 629, 664, 680, 748, 832, 836 ], [ 571, 581, 608, 665, 691, 749, 782, 833 ], [ 582, 585, 609, 666, 730, 750, 807, 834 ], [ 574, 583, 610, 667, 693, 751, 822, 835 ], [ 559, 584, 662, 668, 734, 752, 772, 836 ], [ 561, 585, 669, 670, 736, 753, 789, 837 ], [ 573, 586, 624, 670, 692, 754, 784, 838 ] ] }, "distance": { "d": 6, "X": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 6, 29, 45, 122, 206 ] }, "Z": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 5, 26, 32, 278, 514 ] } }, "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 84. L_g[t,u]=1 iff u=g*t; R_h[t,u]=1 iff u=t*h. A=[I+L5,I+L6,I+L35]; B=[I+R6,I+R24,I+R43], binary sums. Nine VV(k,j) blocks indexed 3*k+j precede one CC block, each size 84. 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, 249 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, 498 checks and total incidence 3984.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }