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"distance": { "d": 50, "X": { "value": 50, "confidence": "upper_bound", "witness": [ 13, 27, 41, 55, 69, 83, 97, 111, 125, 139, 153, 167, 181, 195, 209, 223, 237, 251, 265, 279, 293, 307, 321, 335, 349, 360, 374, 388, 402, 416, 430, 444, 458, 472, 486, 500, 514, 528, 542, 556, 570, 584, 598, 612, 626, 640, 654, 668, 682, 696 ], "witness_provenance": { "found_by": [ "@MathysRennela", "@MicheldeMessieres" ], "date": "2026-10-08", "found_at_samples": 1, "tool": "orbit-restricted SAT; over-claim first reported by @MicheldeMessieres" } }, "Z": { "value": 50, "confidence": "upper_bound", "witness": [ 4, 18, 32, 46, 60, 74, 88, 102, 116, 130, 144, 158, 172, 186, 200, 214, 228, 242, 256, 270, 284, 298, 312, 326, 340, 351, 365, 379, 393, 407, 421, 435, 449, 463, 477, 491, 505, 519, 533, 547, 561, 575, 589, 603, 617, 631, 645, 659, 673, 687 ], "witness_provenance": { "found_by": [ "@MathysRennela", "@MicheldeMessieres" ], "date": "2026-10-08", "found_at_samples": 1, "tool": "perm-transfer of the corrected side's witness (#2755)" } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^350 - 1 with a(x) = x^9 + x^36 + x^48 + x^170 + x^214 + x^227 + x^245 + x^320 + x^324, b(x) = x^5 + x^23 + x^72 + x^101 + x^112 + x^142 + x^230 + x^270 + x^309; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-10-02", "notes": "Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed. Distance over-claim independently reported by @MathysRennela and @MicheldeMessieres on 2026-10-08 (see issue #2899); corrected to d <= 50 with a witness from the maintainers' orbit-restricted search." }, "family": "generalized-bicycle" }