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{ "found_by": [ "@FarLab", "@MathysRennela", "@MicheldeMessieres" ], "date": "2026-10-09", "found_at_samples": 50000, "seeds": [ 101 ], "tool": "orbit-fold (verify/heuristic_distance.py, PR #2902)" } }, "Z": { "value": 50, "confidence": "upper_bound", "witness": [ 14, 20, 25, 35, 36, 60, 81, 92, 97, 107, 113, 117, 118, 129, 135, 169, 205, 206, 215, 216, 228, 277, 293, 299, 334, 339, 343, 346, 351, 365, 390, 402, 405, 420, 427, 464, 467, 482, 499, 501, 526, 545, 552, 554, 588, 614, 622, 623, 661, 678 ], "witness_provenance": { "found_by": [ "@FarLab", "@MathysRennela", "@MicheldeMessieres" ], "date": "2026-10-09", "found_at_samples": 50000, "seeds": [ 101 ], "tool": "orbit-fold (verify/heuristic_distance.py, PR #2902)" } } }, "provenance": { "authors": [ "@vaibhav-baj" ], "construction": "Cyclic generalized-bicycle code over Z_341: H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T], with a={2,64,74,110,178,240,308,322} (weight 8, invariant under j->32j mod 341: fixed points 110, 308 and pair-orbits {2,64},{74,322},{178,240}) and b=a(x^4)={4j mod 341 : j in a}={8,30,99,209,256,265,278,296}, a Frobenius image with the same zero set. Shared divisor (x+1) * six full-order decics of x^341-1 (degree 61), so k=122; both check weights 8 (w=16). First hit of a weight-8 symmetric-word sampler (method in the note); 2M-trial RIS ladder bound 86, then fresh-seed accelerated RIS trials (lightest logical: weight 85, found independently in three 1M-trial chunks).", "origin": "submission", "date": "2026-10-07", "model": "Claude Fable 5.1 (Claude Code)", "search_budget": { "candidates_screened": 3, "ris_trials_per_side": 6000000, "cpu_hours": 28, "tool": "symmetric-word sampler with GF(1024) zero sets + gf2_fast accelerator" }, "notes": "Distance over-claim independently reported by @MathysRennela and @MicheldeMessieres on 2026-10-08 (see issue #2899); corrected to d <= 55 with a witness from the maintainers' orbit-restricted search. Tightened to d <= 44 on 2026-10-09 by @FarLab with the orbit-fold search of PR #2902 (50,000 trials per folded code) while landing correction PR #2933, whose merge had not reached main (issue #2949)." }, "family": "generalized-bicycle" }