By Weil's criterion the Riemann Hypothesis (RH) is equivalent to positivity of the Hermitian form Q of the explicit formula. We show that this is the same as unitarity (absence of negative-norm "ghost" directions) of the logarithmic scaling flow on test functions; the negative index of Q equals the number of zeros off the critical line. This volume does not prove RH. It reformulates and localizes this single obstruction: along the de Bruijn-Newman heat flow; in function-field and Iwasawa models, where positivity is a theorem; as an action principle whose stationary points are closed orbits; in a semilocal structural trace on finite sets of places; as Lax-Phillips / Pavlov-Faddeev cusp scattering, where we prove ||Z_t|| = 1 for all t unconditionally; through a zero-free intertwiner identifying cusp height with the prime cutoff; by damping to abscissa sigma > 1/2; and by computer-assisted positivity (Arb ball arithmetic) of the Weil form on all windows of length <= log 3. A ghost-index calculus gives explicit detection lengths for off-line zeros and shows that current window certificates exclude none. A statement of intellectual honesty and a statement-by-statement rigor audit separate what is proved, cited, computer-assisted, numerical or heuristic. The remaining obstruction is window positivity for every window length, equivalently a positive structural trace realizing the Weil distribution without reference to the zeros.