The Inflationary Parameters as Geometric Signatures of the Universal Cascade Law: A Derivation from Stellar-Scale Measurements via Inter-Scale Geometric Architecture

Description / Abstract: The Universal Cascade Law (Randolph, 2026a) predicts identical geometric architecture at every scale of the self-application hierarchy. Paper III (Randolph, 2026c) predicted that inflationary parameters should be derivable from the geometry of the dual attractor basin transition — stated as a specific, falsifiable prediction. This paper delivers that prediction. 50,000 stars from Gaia DR3, already confirmed as organizing in dual attractor basins at p