Variational Backbone and Regime Closures V (Mass): Core-Density Schur Reduction and the Order-Zero Spectral Mass Shift

This paper treats mass-like gaps in VBRC as summary-interface footprints rather than as primitive coefficients. Starting from the fixed core density of Parts I-II, Part V computes the Schur-reduced retained operator on the retained-effective variables: the retained field and its licensed summary. The unread coordinate appears only through a declared representative pullback, not as an independently observable hidden-sector degree of freedom. At an R2-selected effective background, Schur elimination of the summary-side variation produces an effective retained operator with a projector-valued order-zero footprint. The mass or gap is not this footprint itself, but the lowest positive spectral value of the effective retained operator on the physical retained subspace. R3 then provides only the dispersion check. Part V is therefore a calculation of a summary-mediated spectral gap, not a theory of primitive mass insertion or a unique hidden-sector ontology.