Metric Pressure from Residue Comparison: Quadratic Size, Dualization, and the Dynamical Slot

Metric and dualization are forced by refinement-stable residue comparison. This paper derives a quadratic size functional for curvature residues from the requirement that magnitude comparisons remain stable under refinement and gauge relabeling without word-explosion. A polarization cross-term then pressures an inner-product-like pairing at the curvature tier. A type-mismatch between loop/2-step curvature residues and boundary/source bookkeeping forces a dualization operator (a corridor ancestor of the Hodge star). Together these yield a forced dynamical slot of the form D(*F)=J, interpreted at the stabilized tier, without assuming manifolds, calculus limits, or differential forms as primitives.