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"verify/gate_changed.py RIS-fast (gf2_fast.distance_rand_witness)", "seeds": [ 2066025485 ] } }, "Z": { "value": 77, "confidence": "upper_bound", "witness": [ 6, 7, 8, 18, 20, 22, 25, 26, 27, 28, 34, 36, 37, 39, 40, 41, 43, 45, 59, 64, 71, 76, 78, 84, 86, 88, 95, 101, 103, 114, 122, 125, 132, 138, 140, 150, 161, 163, 164, 165, 169, 173, 181, 188, 190, 192, 194, 197, 198, 204, 216, 219, 222, 234, 239, 240, 262, 263, 271, 293, 306, 315, 344, 350, 400, 403, 409, 435, 491, 497, 508, 514, 528, 543, 580, 584, 617 ], "witness_provenance": { "found_by": [ "@diogoff" ], "date": "2026-09-29", "found_at_samples": 2000000, "tool": "verify/ris_gpu.py recover mode", "seeds": [ 1317976217 ] } } }, "provenance": { "authors": [ "@diogoff" ], "construction": "Cyclic generalized bicycle on Z_323: H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T]; a=[33,43,46,63,69,80,81,90,111,148,149,164,176,202,204,244], b=[13,51,55,67,118,135,146,152,169,186,207,220,237,254,264,305].", "references": [ "arXiv:2306.16400" ], "date": "2026-09-29", "notes": "The trusted board gate found no exact duplicate or Weisfeiler-Leman-equivalent board entry. This does not establish literature novelty; literature novelty remains unverified. Revised after CI circulant-GB structural refutation: a weight-48 X logical was found (seed 1317976216), lowering d<=76 to d<=48. Revised again after CI's RIS-fast pass (gf2_fast.distance_rand_witness, pair_depth=8, seed 2066025485) found a weight-26 X logical at 8,000,000 trials, lowering d<=48 to d<=26. Revised by CI on 2026-09-30: RIS-fast found a weight-26 X logical at 8,000,000 trials (seed 2066025485), lowering d<=48 to d<=26. The supplied support is the X witness.", "model": "GPT-6 Luna", "origin": "submission", "search_budget": { "candidates_screened": 390, "ris_trials_per_side": 8000000, "tool": "research/cyclic_gb.py with gf2_fast; CUDA verify/ris_gpu.py", "notes": "390 cyclic-GB pairs screened at 4,000 RIS trials after five fertile degree-80 ideals. CI RIS-fast found the submitted weight-26 X witness at 8,000,000 trials (seed 2066025485); the prior 2,000,000-trial CUDA search missed it." } }, "family": "generalized-bicycle" }