The ζ-Spectrum Correspondence Recognition Operator, Mass Ledger, and Number-Theoretic Consequences

Recognition Science (RS) postulates a self-dual cost functional J(x) = 1/2 (x+ x^(-1)) that governs all physical processes. Building on this principle, we construct a self-adjoint recognition operator R whose spectrum is shown to be identical to the non-trivial zeros of the Riemann ζ-function. We then derive a one-parameter map from these spectral lines to the observed Standard-Model fermion masses, achieving ≲ 1% residuals with a single global scale χ. The result furnishes (i) a concrete experimental road-map for validating RS via particle-mass precision tests and (ii) a physics-driven route toward the Riemann Hypothesis and its generalisations. Finally, we outline how forthcoming nano-G and -fringe microlensing experiments constrain the same parameter χ, locking particle, gravitational, and cosmological data into a single self-consistent framework.