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68, 81, 98, 102, 126, 139, 150, 153, 156, 177, 187, 190, 232, 233, 234, 235, 245, 296, 318, 319, 345, 346, 347, 354, 368, 369, 370 ] }, "Z": { "value": 30, "confidence": "exact", "witness": [ 7, 25, 26, 27, 55, 56, 57, 62, 63, 64, 65, 66, 67, 117, 150, 166, 177, 178, 179, 205, 235, 255, 272, 285, 309, 314, 331, 344, 347, 368 ] } }, "provenance": { "authors": [ "@seunomonije" ], "construction": "Generalized bicycle on the circulant ring Z_197: H_X = [B^T | A^T], H_Z = [A | B] with A = circ(a), B = circ(b), a = [0, 17, 30, 54], b = [0, 1]. Found by search over GB polynomial supports; distance proven exact by exhaustive DFS refutation (EMPTY at W = 29, 221,881,674,422 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" }