Variational Backbone and Regime Closures V: Mass from Variational Spectra and Higgs as an Effective Card Schur complement, projector-valued order-0 terms, and regime closure

This paper fixes a structural mass mechanism within the series contract “one fixedspatial density e(·) + three operational readings (R1/R2/R3)”. Mass is defined as order-0spectral data of the R1 Hessian at an R2-selected vacuum, equivalently as the dispersionspectrum of the R3 time-completed representative. For the canonical first-derivative backbone,eliminating the closed variable G = DI II forces the Schur term −(η2/α)PRan, an order-0projector correction that preserves the Laplace spine and shifts active channels. After KGnormalization, the dimensionless shift is expressed by the series invariant η2/(αβ) = κ2. Westate the operator-theoretic gates behind “order-0” and self-adjointness, and demonstratede Rham channel selectivity (exact-only action) via a one-page torus computation. Higgsparameters are treated as a card-level factorization of the extracted mass matrix.