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658, 659, 775, 785, 809 ], [ 660, 661, 662, 663, 776, 784, 808 ], [ 664, 665, 666, 667, 777, 783, 807 ], [ 668, 669, 670, 671, 778, 782, 806 ], [ 672, 673, 674, 675, 781, 796, 805 ], [ 676, 677, 678, 679, 780, 795, 804 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 4, 5, 76, 77, 136, 137, 168, 169, 248, 249, 388, 389, 396, 397, 416, 417, 440, 441, 628, 629 ] }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 116, 117, 408, 409, 420, 421, 480, 481, 496, 497, 552, 553, 556, 557, 616, 617, 628, 629, 676, 677 ] } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "One [[4,2,2]] distance-amplification step (CSS tensor product, central three-term truncation, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[170,16,10]] weight-6 two-block generalized bicycle on Z_85 entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 834, k' = 2k = 32, 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 20/20); the doubled distance is certified by the logical-overlap criterion (d' >= 2d) and no lighter logical was found in a 100,000-trial accelerator search on the first-tier candidates of the same family. Base provenance: Generalized bicycle (two-block) code on Z_85: H_X=[A|B], H_Z=[B^T|A^T], a(x)=x^8+x^33+x^46, b(x)=x^3+x^18+x^70; g=gcd(a,b,x^85-1) irreducible of degree 8, k=2*deg(g)=16, row weight 6. Full circulant check sets kept (redundant rows carry the symmetry).", "references": [ "arXiv:2609.37231", "arXiv:2203.17216", "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" }