We present a fully deterministic, operator-theoretic framework for the Riemann Hypothesis(RH), integrating a canonical Hamiltonian construction with a Standing/Sitting Band (SSB)method for prime propagation. By systematically seating composites and propagating standingprimes, the SSB framework guarantees no material clumping of primes, a key limitation of priorapproaches. Gaussian test functions and prime-localized quadratic forms are used to rigorouslycontrol trace contributions, ensuring that any hypothetical off-critical zero violates trace positivity.This humble, fully constructive proof unifies combinatorial, analytic, and operator-theoretictechniques to provide a compelling path through the “eye of the needle” to RH.