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"@TimoKellerMath" ], "origin": "submission", "novelty": "unknown", "construction": "One [[4,2,2]] distance-amplification step (Liang, Gu, Chen, Eisert, Wang, arXiv:2609.37231, Eqs. (14), (15); amplifier checks G_X = G_Z = the all-one row of length 4) applied to the board entry codes/185-65-5.json ([[185,65,5]], a code-calculus E-PUNCTURE transform of 186-64-6; d_X = d_Z = 5), keeping all 60 of its checks.X and all 60 of its checks.Z (linearly independent), in their order. Qubits: central (q,a) -> 4q+a (q a base qubit, 0 <= a < 4); t_j -> 740+j for the j-th Z-check z_j; s_i -> 800+i for the i-th X-check c_i. X-checks: (c_i,a) = {4q+a : q in c_i} + {s_i} (i, then a), then (q) = {4q,...,4q+3} + {t_j : q in z_j} (q = 0..184); Z-checks: (z_j,a) = {4q+a : q in z_j} + {t_j}, then (q) = {4q,...,4q+3} + {s_i : q in c_i}. n = 4*185 + 60 + 60 = 860 = 5n - k of the base, k = 2*65 = 130, check weight 7.", "references": [ "arXiv:2609.37231", "arXiv:1512.07081", "arXiv:2611.08247" ], "date": "2026-11-10", "model": "Claude Opus 5.5", "notes": "Distance: d_X = d_Z = 10 exactly, certified directly by tropidist b03ec2d4077f in certs/860-130-10.json (same pull request), and proved: d_P = 2 d_P(base) for P = X, Z by Lemma 4 of arXiv:2609.37231 (proof in the coordinates of this entry: Proposition 9 of two-block-and-amplified-codes/README.md, github.com/TimoKellerMath/quantum-error-correction @ aaa18674c9a1), and d_X = d_Z = 5 for the base 185-65-5, which has no board certificate, is certified exactly in the same package by two exhaustive search programs (exactA, exactB). Witnesses: u (x) (e_0 + e_1) for the witnesses u of codes/185-65-5.json. At board commit 8042f9da no CSS entry dominates or equals this code in (n, k, d, w), and no entry has its n and k; it is on the frontier only through its check weight 7, since entries of check weight 8 such as 512-132-14 are better in n, k and d. Checked, not equivalent to an existing entry." }, "family": "distance-amplified" }