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638 ] ] }, "distance": { "d": 7, "X": { "value": 7, "confidence": "upper_bound", "witness": [ 0, 48, 80, 305, 336, 384, 592 ] }, "Z": { "value": 7, "confidence": "upper_bound", "witness": [ 0, 16, 32, 144, 160, 384, 544 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "G=C16 semidirect_3 C8, a^16=b^8=1, b*a*b^-1=a^3. Normal form a^i b^j has index i+16j; multiply(i,j)(k,l)=(i+3^j*k mod16,j+l mod8). Set row-action L_g[t,u]=1 iff u=g*t and R_h[t,u]=1 iff u=t*h. A=[I+L_16,I+L_17], B=[I+R_48,I+R_49]. BlocksVV(k,j) indexed2k+j, thenCC, all size128. 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.", "references": [ "https://arxiv.org/abs/2111.03654", "https://arxiv.org/abs/2607.28795", "https://arxiv.org/abs/2607.27644" ], "date": "2026-10-17", "notes": "Displayed presentation: maximum check weight 6, maximum qubit degree 8, 508 checks and total incidence 3048.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }