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491, 493, 508, 512, 515, 534, 537, 545, 556, 559, 567 ], [ 448, 449, 450, 464, 471, 472, 488, 492, 494, 509, 513, 516, 535, 538, 546, 557, 560, 568 ], [ 449, 450, 451, 465, 472, 473, 489, 493, 495, 510, 514, 517, 536, 539, 547, 558, 561, 569 ], [ 450, 451, 452, 466, 473, 474, 490, 494, 496, 511, 515, 518, 537, 540, 548, 559, 562, 570 ], [ 451, 452, 453, 467, 474, 475, 491, 495, 497, 512, 516, 519, 538, 541, 549, 560, 563, 571 ], [ 452, 453, 454, 468, 475, 476, 492, 496, 498, 513, 517, 520, 528, 539, 542, 550, 561, 564 ], [ 453, 454, 455, 469, 476, 477, 493, 497, 499, 514, 518, 521, 529, 540, 543, 551, 562, 565 ], [ 454, 455, 456, 470, 477, 478, 494, 498, 500, 515, 519, 522, 530, 541, 544, 552, 563, 566 ], [ 455, 456, 457, 471, 478, 479, 495, 499, 501, 516, 520, 523, 531, 542, 545, 553, 564, 567 ], [ 456, 457, 458, 472, 479, 480, 496, 500, 502, 517, 521, 524, 532, 543, 546, 554, 565, 568 ], [ 457, 458, 459, 473, 480, 481, 497, 501, 503, 518, 522, 525, 533, 544, 547, 555, 566, 569 ], [ 458, 459, 460, 474, 481, 482, 498, 502, 504, 519, 523, 526, 534, 545, 548, 556, 567, 570 ], [ 459, 460, 461, 475, 482, 483, 499, 503, 505, 520, 524, 527, 535, 546, 549, 557, 568, 571 ] ] }, "distance": { "d": 6, "X": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 132, 264, 396, 528, 550 ] }, "Z": { "value": 6, "confidence": "upper_bound", "witness": [ 0, 132, 264, 396, 528, 550 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "G=C22, product x+y modulo22. L_g[t,u]=1 iff u=g+t; R_h[t,u]=1 iff u=t+h. A is1x5 with support triples[[0, 1, 2], [0, 1, 8], [0, 2, 6], [0, 3, 7], [0, 3, 14]]; B is1x5 with support triples[[0, 1, 2], [0, 1, 8], [0, 2, 6], [0, 3, 7], [0, 3, 14]]; sum the corresponding left or right permutation matrices overF2. Twenty-five VV(k,j) blocks indexed5*k+j precede one CC block, eachsize22. X(j) places A(k) on VV(k,j) and B(j) on CC. Z(k) places B(j)^T on VV(k,j) and A(k)^T on CC. All110 original rows in each sector are independent and retained.", "references": [ "https://arxiv.org/abs/2111.03654", "https://arxiv.org/abs/2607.28795" ], "date": "2026-10-17", "notes": "Displayed presentation: maximum check weight 18, maximum qubit degree 30, 220 checks and total incidence 3960.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }