he Schur-Partitioned Clifford Spectral Localizer: Unifying Prime-Composite Hilbert Space Completeness and Topological Zero Exclusion on the Modular Cusp

Volume XXX (Route S) of the Semilocal Weil Positivity Series. Synthesizes Volume XXVIII (non-commutative Clifford spectral localizer and topological zero exclusion) and Volume XXIX (Prime-Composite Zeta Duality and Beurling-Nyman Hilbert space completeness) into an exact operator identity. Establishes exact block-diagonality of the modular cusp coordinate, Haynsworth signature additivity sig(L) = 0, and the Courant-Fischer variational bridge connecting composite Schur variance reduction to the Gram matrix spectral floor. Certified across scales N = 8 to 128 under a strict zero-free firewall (ZERO_INPUT_COUNT == 0).