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319, 320 ] }, "Z": { "value": 32, "confidence": "upper_bound", "witness": [ 10, 11, 12, 20, 23, 45, 56, 63, 75, 77, 79, 90, 109, 113, 119, 125, 126, 133, 142, 143, 152, 204, 208, 213, 222, 226, 247, 248, 257, 303, 317, 326 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^165 - 1 with a(x) = x^18 + x^47 + x^81 + x^150, b(x) = x^13 + x^23 + x^118 + x^156; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-21", "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." }, "family": "generalized-bicycle" }