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648, 657, 665, 668, 676 ], [ 506, 508, 512, 515, 517, 533, 534, 538, 551, 557, 571, 576, 589, 592, 597, 610, 614, 621, 630, 637, 649, 658, 666, 669, 677 ], [ 507, 509, 513, 516, 518, 534, 535, 539, 552, 558, 572, 577, 590, 593, 598, 611, 615, 622, 631, 638, 650, 659, 667, 670, 678 ], [ 508, 510, 514, 517, 519, 535, 536, 540, 553, 559, 573, 578, 591, 594, 599, 612, 616, 623, 632, 639, 651, 660, 668, 671, 679 ] ] }, "distance": { "d": 10, "X": { "value": 10, "confidence": "upper_bound", "witness": [ 0, 6, 19, 23, 24, 40, 42, 45, 49, 51 ] }, "Z": { "value": 10, "confidence": "upper_bound", "witness": [ 0, 18, 24, 25, 33, 160, 183, 185, 186, 197 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "C40 scalar1x4 cross product. X[j,r]: VV(k,j,r+g),g in A_k; CC(r+g),g in B_j. Z[k,r]: VV(k,j,r-g),g in B_j; CC(r-g),g in A_k. A supports=[[0, 3, 14, 15, 17], [0, 7, 15, 16, 22], [0, 12, 19, 21, 27], [0, 8, 11, 19, 28]]; B supports=[[0, 2, 5, 9, 11], [0, 6, 19, 23, 24], [0, 5, 8, 21, 26], [0, 7, 16, 23, 27]]. Every individual entry is invertible.", "references": [ "https://arxiv.org/abs/2111.03654" ], "date": "2026-10-18", "notes": "Displayed presentation: maximum check weight 25, maximum qubit degree 40, 320 checks and total incidence 8000.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }