Abstract

This paper fixes a structural mass mechanism within the series contract “one fixed spatial density e(·) + three operational readings (R1/R2/R3)”. Mass is defined as order-0 spectral data of the R1 Hessian at an R2-selected vacuum, equivalently as dispersion data of the R3 time-completed representative. For the canonical first-derivative backbone, eliminating the closed variable F := DI II induces, on the open sector, a Schur complement correction of the form −(η 2/α)PRan: an order-0 projector term that preserves the Laplace-type principal operator and shifts active channels. Elimination and the resulting Schur/projector term are representation-level implementations of a declared readout/retention protocol (Part IV); they do not modify the fixed backbone or its principal operator. After KG normalization, the dimensionless shift is expressed by the series invariant η 2/(αβ) = κ 2 . We state the operatortheoretic gates behind “order-0” and self-adjointness, demonstrate de Rham channel selectivity (exact-only action) via a one-page torus computation, and position Higgs parameters as a representation-level factorization of the extracted mass matrix.