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"X": { "value": 95, "confidence": "upper_bound", "witness": [ 2, 13, 19, 21, 22, 24, 26, 31, 38, 39, 42, 49, 59, 60, 62, 64, 67, 72, 74, 75, 77, 80, 83, 86, 88, 89, 92, 93, 97, 110, 112, 115, 119, 120, 122, 127, 129, 131, 132, 141, 143, 145, 146, 150, 151, 161, 162, 164, 174, 177, 186, 192, 195, 196, 204, 209, 214, 223, 229, 231, 232, 233, 235, 242, 243, 247, 249, 251, 252, 259, 262, 263, 264, 270, 276, 280, 284, 289, 290, 291, 292, 297, 308, 324, 330, 348, 349, 356, 376, 378, 386, 431, 495, 603, 611 ], "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": 96, "confidence": "upper_bound", "witness": [ 3, 6, 9, 12, 15, 23, 27, 36, 44, 46, 47, 49, 51, 58, 59, 66, 67, 69, 76, 78, 80, 81, 87, 96, 100, 102, 103, 114, 115, 122, 124, 126, 127, 129, 133, 134, 136, 137, 149, 150, 153, 158, 164, 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Zero-set design after arXiv:2609.22503 (BCH run-length floors); construction family per arXiv:1904.02703. a=[122, 134, 163, 259, 301, 312]; b=[8, 66, 114, 169, 257, 312].", "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" }