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588, 590 ], [ 500, 501, 502, 503, 564, 565, 570, 604 ] ] }, "distance": { "d": 28, "X": { "value": 28, "confidence": "upper_bound", "witness": [ 0, 1, 16, 17, 32, 33, 60, 61, 88, 89, 112, 113, 204, 205, 324, 325, 360, 361, 368, 369, 408, 409, 432, 433, 440, 441, 460, 461 ] }, "Z": { "value": 28, "confidence": "upper_bound", "witness": [ 28, 29, 72, 73, 104, 105, 124, 125, 156, 157, 160, 161, 180, 181, 224, 225, 304, 305, 308, 309, 396, 397, 428, 429, 472, 473, 492, 493 ] } }, "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 [[126,18,14]] weight-10 cyclic GB, N=63 entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 612, k' = 2k = 36, check weight w' = w+1 = 11. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 28/28); a 100000-trial fast-backend search (seed 5000) found nothing lighter (min weight 28). Base provenance: Generalized bicycle (2BGA on Z_63), circulant size 63, a(x) = 1 + x^14 + x^16 + x^21 + x^27, b(x) = 1 + x^31 + x^39 + x^40 + x^45. Weight-5 supports designed as multiples of a degree-9 divisor g of x^N-1 (k = 2 deg g). Check weight 10 (weight-9plus cell).", "references": [ "arXiv:2609.37231", "arXiv:1904.02703", "arXiv:2306.16400" ], "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" }