The Phase Geometry Papers: A 4D Mechanical Solution to the Hierarchy Problem

P.I
Theoretical Framework

The Succession of Lineage

Exploring the mapping of Randall-Sundrum 5D warped geometry into a 4D scale-dependent phase transition governed by the Gravitational Reynolds Number.

$Equation Alpha$

P.II
Empirical Case Study

Quantitative analysis of the 300 kpc "Governance Barrier" in massive galaxy clusters and its role in the bifurcation of Ultra-Diffuse Galaxies.

$Equation Suppression$

P.III
Computational Proof

Mechanical verification via High-Resolution LBM simulations, proving the emergence of the 0.35 modularity plateau as a stability limit.

$Equation Stability$