Local IR-Regularization of STDM: Geometric Resolution of the Hubble Tension Based on Phase Boundaries and Scale-Dependent Vacuum Elasticity in Cosmic Voids

Abstract & Project Description:This repository contains the official research preprint and validation computational core (Void-Engine v5.3) establishing the localized infrared (IR) regularization framework within the Special Theory of Dark Matter (STDM). This research node delivers a simultaneous analytical resolution to two of the most critical crises in modern cosmology: the 5σ Hubble tension—the discrepancy between global Planck baseline data (67.4 km/s/Mpc) and local SH0ES supernova measurements (73.2–74.0 km/s/Mpc)—and the fatal gradient catastrophes (NaN solver overflows) that inherently destabilize classical General Relativity (GR) tensors inside low-density cosmic underdensities. Bypassing phenomenological parameter-tuning, artificial constants, or the postulation of undetected dark sector particles, this work introduces a non-linear, singularity-free analytical solution rooted in high-dimensional exceptional E8 Lie lattice topologies. We formalize a dynamic vacuum screening function, kappa_eff(rho_b) = (28/248) * exp(-gamma * rho_b), which modulates the scale-dependent vacuum elasticity as a function of the local environmental baryon density field. Key Mathematical Insights & Axiomatic Theorems:1. Pristine Cosmic Voids (rho_b -> 0): The sub-Planckian vacuum substrate undergoes unshielded thermodynamic relaxation toward its algebraic E8 symmetry ceiling (~0.1129), driving the emergent metric refraction index (n_STDM) to naturally generate the local 73.2–73.4 km/s/Mpc expansion plateau verified by late-Universe observations.2. Baryonic Screening Frontiers (rho_b -> infinity): Ambient mass-energy structures execute a complete phase-fluctuation collapse, exponentially suppressing active vacuum boiling (kappa_eff -> 0) and securing a flawless asymptotic convergence with standard Einsteinian GR.3. Axiomatic Regularization: By replacing discontinuous differential tensor products with a proprietary connected sum gluing operator (#Ush), the algorithm stabilizes coordinate boundaries, mapping a distinct topological pinch-off transition (hyperboloid "waist" profile) at the H0 ≈ 69 km/s/Mpc equilibrium threshold. Replication Package Contents:- Local_IR_Regularization_STDM.pdf — Full-text Research Preprint (optimized for REVTeX-4.2 standards).- CRYSTALINTEGRATION.py — Raw, uncompressed Python verification script executing the strict 133-configuration matrix (19 spatial scale intervals and 7 prime-ordered baryonic depletion steps to eliminate numerical aliasing and false lattice resonances). Keywords: Hubble Tension; Cosmic Voids; Exceptional Lie Algebra E8; Vacuum Elasticity; Metric Refraction; Infrared Regularization; Open-Source Astrophysics; Void-Engine Core.