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493, 498, 502, 504, 520, 530, 537, 542, 543, 559, 568, 573, 580, 582, 596, 605, 617, 620, 621, 633, 645, 651, 653, 660 ], [ 488, 494, 499, 503, 505, 521, 531, 538, 543, 544, 560, 569, 574, 581, 583, 597, 606, 618, 621, 622, 634, 646, 652, 654, 661 ], [ 489, 495, 500, 504, 506, 522, 532, 539, 544, 545, 561, 570, 575, 582, 584, 598, 607, 619, 622, 623, 635, 647, 653, 655, 662 ] ] }, "distance": { "d": 10, "X": { "value": 10, "confidence": "upper_bound", "witness": [ 0, 1, 6, 13, 23, 39, 41, 45, 50, 56 ] }, "Z": { "value": 10, "confidence": "upper_bound", "witness": [ 0, 17, 23, 24, 32, 156, 178, 180, 181, 192 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "C39 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, 6, 11, 19, 22], [0, 7, 9, 15, 27]]; B supports=[[0, 2, 6, 11, 17], [0, 1, 6, 13, 23], [0, 2, 9, 14, 23], [0, 1, 4, 16, 25]]. 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, 312 checks and total incidence 7800.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }