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} }, "Z": { "value": 35, "confidence": "upper_bound", "witness": [ 0, 341, 367, 394, 418, 431, 433, 456, 474, 489, 491, 493, 505, 506, 520, 521, 530, 557, 586, 592, 594, 596, 611, 613, 617, 618, 644, 645, 648, 650, 658, 673, 679, 680, 681 ], "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={0,11,4,128,74,322} (weight 6, invariant under j->32j mod 341: fixed points 0, 11 and pair-orbits {4,128}, {74,322}) and b=a(x^8)={0,1,32,88,189,251}, a shifted Frobenius image with the same zero set. Shared divisor (x+1) times four full-order decics of x^341-1 (degree 41), so k=82; both check weights 12. Found by exhaustive enumeration of all 987,350 symmetric weight-6 words with exact zero sets in GF(1024) (433 equivalence classes), RIS-screened and laddered to 10,000,000 trials per side.", "origin": "submission", "date": "2026-10-07", "model": "Claude Fable 5.1 (Claude Code)", "search_budget": { "candidates_screened": 120, "ris_trials_per_side": 10000000, "cpu_hours": 30.0 }, "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 <= 35 on 2026-10-09 by @FarLab with the orbit-fold search of PR #2902 (50,000 trials per folded code) while landing correction PR #2934, whose merge had not reached main (issue #2949)." }, "family": "generalized-bicycle" }