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"confidence": "upper_bound", "witness": [ 0, 2, 8, 87, 296, 346 ] } }, "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 96. L_g[t,u]=1 iff u=g*t; R_h[t,u]=1 iff u=t*h. A=[I+L2,I+L3,I+L16]; B=[I+R2,I+R3,I+R22], binary sums. Nine VV(k,j) blocks indexed 3*k+j precede one CC block, each size 96. 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, 285 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, 570 checks and total incidence 4560.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }