Volumetric Calculus: Mathematical Reference for the Theory of Expanding Matter

This document is the reference source for the mathematics used in the Theory of Expanding Matter. It contains the complete formulation of the Volumetric Calculus: the definitions of the volumetric integrals, the construction of the invariant ratio, and the projective rules that govern how fields and volumes are handled in RP³. It presents the operator system used in the theory, including the differential operators, the recursive hierarchy built from them, and the transformations associated with the Noether and closure operations. The document also includes the derivations used to identify the stable outcomes produced by this framework. Everything needed to use the calculus in the rest of TEM is collected here in mathematical form.