Ainta's weighted n-point simple-zero refinement at n = 6, with the Montgomery–Taylor window of the pinned Zeta23 Theorem D replaced by AMTOPA's window (first 13 cosine terms of zeta-exact-pressure, scaled by 4/5). Theorem D's window-dependent parts are re-proved in-file for this window: - admissibility (a certified positive-variation bound); - zero side and prime side (ported from Zeta23's XiPrime/ThmD, Apache-2.0); - the a/b/J limits (incl. an exact integral-swap identity); - the exact constant H_AM = H_MT − Σ c_j²(½ − 1/(4π²j²))/(2 sin²(1/√2)) ≥ 0.6721883; - the retargeted Zeta Lab bridge (MIT). Finite certificate: 14,872 leaves on the half-space g₀ ≤ g₄ (pyramid/slope tests with 200 expansion centres; pyramid table adapted from five-point-pyramid-2 by typh, centres after six-point-convex-basins-2 by typh, Apache-2.0), with a new integer enclosure of the AM pair kernel. κ = 6733143/10⁷ ≤ (H_AM − B(m−5)/m)/(1 − c(m−5)/m) at m = 146. No new axioms. δ 0.002 % and Φ ≥ 0.67
κ = (6733166 : ℝ) / 10000000