{ "schema_version": "0.2", "name": "[[502,102,d<=50]] designed-divisor generalized-bicycle CSS code", "code_type": "CSS", "n": 502, "k": 102, "checks": { "X": [ [ 0, 28, 40, 54, 148, 167, 179, 205, 210, 228, 246, 250, 256, 258, 261, 263, 265, 308, 326, 345, 346, 347, 349, 430 ], [ 0, 1, 29, 41, 55, 149, 168, 180, 206, 211, 229, 247, 257, 259, 262, 264, 266, 309, 327, 346, 347, 348, 350, 431 ], [ 1, 2, 30, 42, 56, 150, 169, 181, 207, 212, 230, 248, 258, 260, 263, 265, 267, 310, 328, 347, 348, 349, 351, 432 ], [ 2, 3, 31, 43, 57, 151, 170, 182, 208, 213, 231, 249, 259, 261, 264, 266, 268, 311, 329, 348, 349, 350, 352, 433 ], [ 3, 4, 32, 44, 58, 152, 171, 183, 209, 214, 232, 250, 260, 262, 265, 267, 269, 312, 330, 349, 350, 351, 353, 434 ], [ 0, 4, 5, 33, 45, 59, 153, 172, 184, 210, 215, 233, 261, 263, 266, 268, 270, 313, 331, 350, 351, 352, 354, 435 ], [ 1, 5, 6, 34, 46, 60, 154, 173, 185, 211, 216, 234, 262, 264, 267, 269, 271, 314, 332, 351, 352, 353, 355, 436 ], [ 2, 6, 7, 35, 47, 61, 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73, 74, 78, 84, 85, 89, 102, 103, 109, 111, 118, 121, 122, 127, 130, 136, 139, 144, 145, 148, 155, 157, 163, 164, 177, 181, 182, 188, 192, 193, 195, 208, 221, 229, 231, 234, 243 ], "witness_provenance": { "found_by": [ "@FarLab" ], "date": "2026-08-19", "found_at_samples": 1000000000, "tool": "ris_gpu", "seeds": [ 88000007 ] } }, "Z": { "value": 50, "confidence": "upper_bound", "witness": [ 1, 3, 7, 10, 14, 16, 24, 33, 36, 38, 46, 59, 72, 74, 75, 79, 85, 86, 90, 103, 104, 110, 112, 119, 122, 123, 128, 131, 137, 140, 145, 146, 149, 156, 158, 164, 165, 178, 182, 183, 189, 193, 194, 196, 209, 222, 230, 232, 235, 244 ], "witness_provenance": { "found_by": [ "@FarLab" ], "date": "2026-08-19", "found_at_samples": 1000000000, "tool": "ris_gpu", "seeds": [ 88000007 ] } } }, "provenance": { "authors": [ "@npdeep" ], "construction": "Generalized-bicycle CSS code over F2[x]/(x^251-1): H_X=[A|B], H_Z=[B^T|A^T], with A=sum_{e in a} P^e, a=[0,1,5,23,41,46,72,84,103,197,211,223], and B=sum_{e in b} P^e, b=[72,153,155,156,157,176,194,237,239,241,244,246].", "references": [ "arXiv:2306.16400" ], "date": "2026-08-13", "notes": "Witness-backed d<=56 only; no exact-distance claim. Distance revised 2026-08-19 by GPU deep refutation with the board's standalone ris_gpu tool (verify/ris_gpu.cu, sqetch kernels by Muzhou Ma, MIT) on an NVIDIA L40S: a 1,000,000,000-trial random-ISD recovery ladder per side (seed 88000007) committed a weight-50 X logical and a weight-50 Z logical, both re-verified on the CPU with the repo's GF(2) arithmetic and recorded here as the new per-side witnesses. This tightens d<=56 to d<=50 and the score from 102*56^2/502 = 637.15 to 102*50^2/502 = 507.97. The distance remains a witness-backed upper bound, not an exact-distance claim. @npdeep constructed the code. Refutation credit and the search budget are recorded in witness_provenance on each corrected side (schema 0.2, issue #611); authorship is unchanged.", "model": "Magic State Labs (Custom) v0.1" }, "family": "generalized-bicycle" }