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270, 272, 288 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 300000000, "survived_samples": 300000000, "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)", "seeds": [ 4102 ] } }, "Z": { "value": 26, "confidence": "upper_bound", "witness": [ 13, 20, 26, 51, 61, 68, 87, 90, 99, 146, 154, 168, 173, 194, 199, 214, 231, 236, 238, 244, 250, 253, 257, 265, 282, 293 ] } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "unknown", "construction": "non-abelian 2BGA (Lin-Pryadko) on the metacyclic group Z_31 |x Z_5 (order 155), n=310; supports a=[71, 10, 56, 148, 67], b=[135, 144, 52, 41, 115] (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." } }