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"upper_bound", "witness": [ 48, 81, 88, 98, 118, 121, 128, 131, 138, 141, 148, 151, 158, 161, 381, 383, 404, 405, 406, 440, 474, 475, 476, 510, 533, 534, 603, 604, 626, 628 ], "witness_provenance": { "found_by": [ "@dorakingx" ], "date": "2026-09-11", "found_at_samples": 1000000, "tool": "gf2_fast RIS (verify/gf2_fast.cpp), both sides searched jointly", "seeds": [ 10670, 859, 1794, 4722, 8890, 7373, 616161, 990002 ], "survived_samples": 20000000 } }, "Z": { "value": 30, "confidence": "upper_bound", "witness": [ 2, 4, 26, 27, 96, 97, 120, 154, 155, 156, 190, 224, 225, 226, 247, 249, 469, 472, 479, 482, 489, 492, 499, 502, 509, 512, 532, 542, 549, 582 ], "witness_provenance": { "found_by": [ "@dorakingx" ], "date": "2026-09-11", "found_at_samples": 1000000, "tool": "mirror of the other side's witness (L(e)<->R(-e)); sides searched jointly", "seeds": [ 10670, 859, 1794, 4722, 8890, 7373, 616161, 990002 ], "survived_samples": 20000000 } } }, "provenance": { "authors": [ "@dorakingx" ], "construction": "Generalized bicycle (two-block) code on Z_315: H_X=[A|B], H_Z=[B^T|A^T] with A, B the 315x315 circulants of a(x)=1+x+x^94, b(x)=1+x^10+x^50 (circulant row u touches qubits u-e mod 315 for each exponent e; right block index offset 315). k = 2*deg gcd(a, b, x^315-1) = 14. Found by exhaustive designed-divisor enumeration of all weight-6 trinomial pairs on Z_N, N=181..350 (k >= 8; 109,888 listed pairs = 102,092 classes under monomial factors, units and swap), then fresh-seed fast-RIS ladders; the distance is a witness-backed upper bound (deepest null result 20000000 trials).", "references": [ "arXiv:1904.02703", "arXiv:2203.17216", "arXiv:2306.16400", "arXiv:2503.03827" ], "date": "2026-09-11", "notes": "Checked, not equivalent to any board entry: the gate reports no exact duplicate and no WL-equivalent entry (WL cannot separate circulant codes, so closed-walk counts of the Tanner graph were compared as well). The board entries with n = 630 are [[630,12,34]] w=6, [[630,126,20]] w=9, [[630,6,36]] w=6, [[630,86,3]] w=4; none shares this k and d. It dominates [[660,8,30]] on (n, k, d, w), which therefore leaves the frontier of every cell the two share. No board entry dominates it on all four axes. The Z witness is the image of the X witness under the two-block symmetry L(e)<->R(-e); the RIS runs searched both sides jointly. Literature novelty unverified.", "novelty": "unknown", "origin": "submission" }, "family": "generalized-bicycle" }