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213, 302, 303, 323, 377, 385, 386, 387, 388, 389, 395, 396, 400, 401, 402, 415, 416 ] }, "Z": { "value": 31, "confidence": "exact", "witness": [ 37, 71, 72, 73, 74, 83, 84, 87, 100, 109, 110, 122, 141, 248, 260, 272, 284, 286, 299, 302, 306, 312, 322, 324, 326, 346, 352, 364, 366, 386, 406 ] } }, "provenance": { "authors": [ "@seunomonije" ], "construction": "Generalized bicycle on the circulant ring Z_211: H_X = [B^T | A^T], H_Z = [A | B] with A = circ(a), B = circ(b), a = [0, 12, 34, 54], b = [0, 1]. Found by search over GB polynomial supports; distance proven exact by exhaustive DFS refutation (EMPTY at W = 30, 564,710,269,711 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" }