Prime Towers, Positive Cones, and a Microlocal Criterion toward RH (Research Note)

We propose a prime‑first refactorization of the Riemann zeta function based on prime towers that aggregate all powers p^m of each prime into a single harmonic block, yielding a transparent decomposition of \zeta(s-ik) and its completed form \xi(s-ik). Inside the cone of even tests with non‑negative cosine transform (Gaussian or Gauss⊛Poisson), the smoothed prime‑side becomes a positive spectral measure on \pm m\log p. In windows |x-1/2|\le\delta the archimedean block provides an explicit \Gamma-floor; with Lipschitz certificates this enables lattice→continuum transfer; a microlocal lemma (T9) yields a universal threshold J_{\max}/a for the impact of an aligned off‑line zero. Together—structural positivity, microlocalization, explicit constants—these support an operational positivity criterion which, if verified across x-windows and t_0-bands (step \le FWHM/3), would exclude off‑line zeros and imply RH. This Research Note fixes the idea, states compact criteria, and outlines a test plan; no final proof is claimed.