Chapter 24: The Spectral Correspondence

We establish the Hilbert–Pólya realization of the Riemann Hypothesis within the τ-framework. The spectral parameter Λ(s) = ι_τ²(s(1-s) - ¼) transforms the critical strip into the spectral domain. If the completed τ-zeta function ζ_τ(s) admits a determinant representation over the lemniscate operator H_L, then every non-trivial zero of ζ_τ corresponds to an eigenvalue of H_L. The determinant representation is the single conjectural step; all consequences are τ-effective. This chapter completes the algebraic-geometric bridge from number theory to spectral geometry.