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"exact", "witness": [ 2, 11, 19, 24, 38, 43, 46, 84, 103, 120, 125, 147, 156, 192, 197, 210, 219, 266, 267, 271, 272, 273, 304, 305, 306, 307, 308, 393, 439, 440, 441, 442, 443 ] }, "Z": { "value": 33, "confidence": "exact", "witness": [ 23, 49, 101, 102, 146, 166, 167, 187, 193, 194, 197, 198, 199, 238, 260, 276, 298, 301, 303, 320, 339, 342, 347, 373, 383, 393, 400, 402, 414, 429, 441, 446, 451 ] } }, "provenance": { "authors": [ "@seunomonije" ], "construction": "Generalized bicycle on the circulant ring Z_227: H_X = [B^T | A^T], H_Z = [A | B] with A = circ(a), B = circ(b), a = [0, 22, 27, 63], b = [0, 1]. Found by search over GB polynomial supports; distance proven exact by exhaustive DFS refutation (EMPTY at W = 32, 3,209,399,834,729 nodes).", "origin": "submission", "novelty": "unknown", "model": "exhaustive verification (exhaustive-qec verifier 0.1.0)", "date": "2026-08-14", "notes": "Distance certified exhaustively, not estimated. Full method, evidence and a re-runnable notebook: https://github.com/qernelkit/verifiable-qec-experiments/blob/main/experiments/qldpc_challenge/qldpc_challenge.ipynb" }, "family": "generalized-bicycle" }