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446, 447, 570, 591 ], [ 448, 449, 450, 451, 553, 571, 592 ], [ 452, 453, 454, 455, 572, 585, 593 ], [ 456, 457, 458, 459, 573, 586, 594 ], [ 460, 461, 462, 463, 574, 587, 595 ], [ 464, 465, 466, 467, 575, 588, 596 ], [ 468, 469, 470, 471, 576, 589, 597 ], [ 472, 473, 474, 475, 577, 590, 599 ], [ 476, 477, 478, 479, 578, 591 ], [ 480, 481, 482, 483, 579, 592, 600 ], [ 484, 485, 486, 487, 580, 593, 601 ], [ 488, 489, 490, 491, 594, 598, 602 ], [ 492, 493, 494, 495, 595, 603 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 4, 5, 44, 45, 60, 61, 92, 93, 140, 141, 220, 221, 460, 461, 476, 477, 480, 481, 488, 489 ] }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 152, 153, 164, 165, 172, 173, 276, 277, 308, 309, 412, 413, 428, 429, 460, 461, 476, 477, 492, 493 ] } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "Distance-amplified code: one [[4,2,2]] tensor-product amplification step (central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[124,10,10]] entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 610, k' = 2k = 20, check weight w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 20/20); a 100000-trial fast-backend search (seed 5000) found nothing lighter (min weight 20). Base provenance: Two-block group-algebra code on the cyclic group Z_62 (elements indexed 0..61); supports a = [0, 59, 2] (left regular representation) and b = [0, 20, 12] (right regular representation); H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] (research/kit/group_algebra.py build_2bga).", "references": [ "arXiv:2609.37231" ], "date": "2026-09-30", "notes": "Constructed and packaged with the Space Bunny Alpha 1.0 model.", "model": "Space Bunny Alpha 1.0" }, "family": "distance-amplified" }