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322, 328, 331 ] ] }, "distance": { "d": 12, "X": { "value": 12, "confidence": "upper_bound", "witness": [ 192, 193, 208, 209, 264, 265, 268, 269, 272, 273, 284, 285 ] }, "Z": { "value": 12, "confidence": "upper_bound", "witness": [ 8, 9, 64, 65, 96, 97, 160, 161, 192, 193, 248, 249 ] } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "Distance-amplified code: one [[4,2,2]] tensor-product amplification step (central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[72,12,6]] bivariate bicycle code entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 348, k' = 2k = 24, check weight w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 12/12); a 100000-trial fast-backend search (seed 5000) found nothing lighter (min weight 12). Base provenance: Bivariate bicycle code, orders (6, 6), A=x**3 + y**2 + y, B=x**2 + x + y**3 (periodic boundary conditions).", "references": [ "arXiv:2609.37231", "arXiv:2308.07915" ], "date": "2026-09-30", "notes": "Constructed and packaged with the Space Bunny Alpha 1.0 model.", "model": "Space Bunny Alpha 1.0" }, "family": "distance-amplified" }