Geometric Origin of All Physical Constants: Unified Derivation of Standard Model Parameters from the Material Contraction Universe Model

Geometric Origin of All Physical Constants (Version 3.0) This version (v3.0) represents a definitive leap in the Material Contraction Universe Model (MCUM). While previous versions established the cosmological framework—resolving dark matter and dark energy through the "purge" mechanism—this update provides a complete, first-principles geometric derivation of the Standard Model parameters. Key breakthroughs in this unified version: Geometric Phase Factor ($\delta = \pi\phi + 1/4$): Derivation of the universal scale factor for mass hierarchy using the circle constant $\pi$ and the golden ratio $\phi$. Lepton Mass Hierarchy: Reproduction of mass ratios (e.g., $m_\mu/m_e \approx e^\delta$) with over 99.7% accuracy, reducing Yukawa couplings to discrete geometric layers. Fine-Structure Constant ($\alpha_{em}$): Geometric derivation of $1/137$ as a manifestation of the scale-gap between the Planck and electron scales ($\alpha_{em} = \sqrt{6} / (e^\delta \phi)$). Parameter Extinction: Demonstrating that the Standard Model's 19 free parameters are not arbitrary values but necessary geometric invariants derived from a single dynamic variable: the Hubble constant ($H_0$).