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865, 892 ], [ 614, 623, 691, 713, 762, 803, 864, 893 ], [ 621, 624, 700, 714, 773, 804, 875, 894 ], [ 622, 625, 701, 715, 771, 805, 874, 895 ], [ 623, 626, 699, 716, 772, 806, 873, 896 ], [ 618, 627, 698, 717, 769, 807, 872, 897 ], [ 619, 628, 696, 718, 770, 808, 871, 898 ] ] }, "distance": { "d": 6, "X": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 9, 87, 102, 158, 214 ] }, "Z": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 9, 12, 353, 552, 627 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "G=S3 x C15. Canonical coordinates(i,j,z), 0<=i<3,0<=j<2,0<=z<15, index i+3*j+6*z. Multiplication (i,j,z)(k,l,t)=(i+(-1)^j*k mod3,j+l mod2,z+t mod15). L_g[t,u]=1 iff u=g*t; R_h[t,u]=1 iff u=t*h. A=[I+L9,I+L22,I+L29]; B=[I+R9,I+R22,I+R41], binary sums. Nine VV(k,j) blocks indexed3*k+j precede one CC block, each size90. X(j) has A(k) onVV(k,j) and B(j) onCC. Z(k) has B(j)^T onVV(k,j) and A(k)^T onCC. Keep first independent original rows,267 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, 534 checks and total incidence 4272.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }