We prove a regularity theorem, called Target T, for the boundary trace of a Dirichlet series with bounded coefficients satisfying a logarithmically-averaged uniform Archimedean cancellation hypothesis on compact intervals of the imaginary axis. Under these hypotheses the boundary trace F (1+it) lies in the inhomogeneous Besov class Bˢ∞, ∞, ₋₎₂ (ℝ) for every s ≥ 0, with explicit control of the local Besov norm on any unit interval by Cₛ √B⌈ₒ+₃/₂⌉, where Bₖ = Σ |aₙ|² (log n) ^2k/n² and Cₛ ≤ Dˢ (s!) ^β for a window-dependent rate D and Gevrey class β > 1 of the compactly supported mollifier. The proof proceeds by a Littlewood–Paley decomposition of the boundary trace as a tempered distribution at σ = 1, a windowed Montgomery–Vaughan L² bound on each dyadic slice with an honest polynomial-in-2ʲ slice factor, and a Meyer wavelet assembly via the Paley–Wiener derivative-transfer identity. The cancellation hypothesis enters only through Tenenbaum-type continuity of the boundary trace, via the Hardy–Karamata Tauberian theorem combined with Abel's continuity theorem; the quantitative analysis is cancellation-free. The hypothesis holds unconditionally for the two-point Liouville correlation gₐ (m) = λ (m) λ (m+h) 𝟙₌≡₀ (ₖ) by Tao's 2016 logarithmic Chowla, via a character decomposition of the residue-class indicator. MSC 2020: Primary 42B35, 46E35. Secondary 11M41, 42C40.
Theodore Deligiannis (Sun,) studied this question.