PRT_pre

This supplementary document expands the theoretical, mathematical, and conceptual foundations of the Processing-Rate Theory (PRT), a minimal scalar extension of General Relativity.It introduces no new dynamical structures beyond PRT; instead, it demonstrates why the theory’s canonical scalar sector, multiplicative effective metric, and strict separation between geometry and rate form the unique internally consistent formulation compatible with Einstein gravity.The supplement develops the foundational principles of rate-based physics, analyzes the spectral hierarchy of deviations in the availability field R(x)R(x), and shows how global relaxation of R(t)R(t) naturally produces the observed dark-matter–like and dark-energy–like phenomenology without modifying curvature.It further presents the dual geometric–informational ontology, establishes the theory’s minimality and inevitability through rigorous no-extension arguments, and details observational predictions including late-time expansion deviations, growth-rate signatures, and lensing effects.Together with the main PRT paper, this supplement provides the complete conceptual and mathematical structure of the Processing-Rate Theory, emphasizing its uniqueness, consistency, and testability.