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441, 447, 449, 454, 461, 523, 525, 549, 617, 622, 644, 656, 670 ] }, "Z": { "value": 34, "confidence": "upper_bound", "witness": [ 0, 9, 42, 67, 106, 123, 148, 228, 229, 233, 234, 235, 249, 261, 310, 318, 325, 326, 336, 362, 453, 460, 480, 486, 503, 512, 550, 553, 557, 569, 605, 629, 632, 659 ] } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "unknown", "construction": "non-abelian 2BGA (Lin-Pryadko) on PGL(2,7) (order 336), n=2|G|=672; supports a=[7, 16, 331, 275], b=[121, 293, 291, 46] (element indices in the kit's BFS/regular enumeration); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T]", "model": "Claude Opus 4.8", "date": "2026-07-24", "notes": "Found by a continual non-abelian 2BGA sweep; distance confirmed at 80M x 3 pd20 RIS (min held) before packaging." } }