Besov regularity of boundary traces of conditionally convergent Dirichlet series

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 B^s∞,∞,loc(ℝ) for every s ≥ 0, with explicit control of the local Besov norm on any unit interval by C_s √B⌈s+3/2⌉, where B_k = Σ |a_n|²(log n)²ᵏ/n² and C_s ≤ D^s (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-2^j 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 g_a(m) = λ(m)λ(m+h)𝟙m≡a(W) by Tao's 2016 logarithmic Chowla, via a character decomposition of the residue-class indicator. MSC 2020: Primary 42B35, 46E35. Secondary 11M41, 42C40.