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506, 523, 644 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "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": 44, "confidence": "upper_bound", "witness": [ 2, 3, 14, 34, 41, 64, 72, 74, 86, 88, 92, 96, 110, 113, 119, 151, 153, 155, 158, 162, 176, 182, 196, 199, 212, 219, 222, 223, 230, 232, 234, 236, 258, 265, 271, 285, 291, 293, 294, 308, 312, 330, 335, 636 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 300000000, "survived_samples": 300000000, "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)", "seeds": [ 4101 ] } } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Cyclic generalized bicycle over Z_337 (n=2m=674): H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T]. a and b are sparse multiples of the BCH-designed divisor g(x) of x^m-1 (g_int=6554608529399; zero-set run 2, complement run 41), found by Prange search inside the ideal (g). Zero-set design after arXiv:2609.22503 (BCH run-length floors); construction family per arXiv:1904.02703. a=[72, 180, 182, 254, 261, 297, 320]; b=[37, 129, 148, 202, 230, 243, 251].", "origin": "submission", "date": "2026-09-22", "model": "GLM 5.3 Flash (Zed agent)", "search_budget": { "candidates_screened": 300, "ris_trials_per_side": 100000, "wall_clock_hours": 3.5, "tool": "research/cyclic_defining_set.py + gf2_fast", "notes": "One sweep over BCH-designed divisor ideals on Z_127 and Z_337 (29 records staged, 10 on the mutual Pareto frontier); per-code deep confirm at 100k RIS trials/side; wall clock shared across the batch and inflated by concurrent campaigns on this machine." }, "notes": "The search_budget tool string names cyclic_defining_set.py under a research/ path; that script is kept in the authors' own repo and is not a file of this repository." }, "family": "generalized-bicycle" }