Unified Mechanical Cosmology (UMC): A Hierarchical EFT of Structure Formation. (Formerly DFE)

This project documents the development and implementation of Unified Mechanical Cosmology (UMC), a two-layer effective field theory designed to resolve the primary tensions of late-time cosmology (H_0 and S_8). The framework provides a mechanical interpretation of the cosmic web, treating the dark sector as a dissipative, viscoelastic medium rather than a scale-free fluid. The Hierarchical Architecture The project is organized into two distinct layers that bridge physical intuition with numerical rigor: Layer 1: Dynamic Filamentary Equilibrium (DFE) [The Morphological Prior] Role: Defines the structural state space and material ontology of the cosmic web. Core Concepts: Tidal tensor classification of filaments and nodes, the "Mist Slurry" primordial state, and the Tension Constant (T_k) as an effective stress scale. Evolution: Originally formulated as a rigid grid cosmology (Revision 3), DFE now serves as the geometric prior for the dynamical layer. Layer 2: Viscoelastic Growth Effective Theory (VGET) [The Dynamical Operator] Role: Provides the operator-valued formalism for structure growth. Implementation: A non-local viscoelastic kernel (\Theta = \{\beta_g, \tau, \epsilon\}) that introduces memory and damping into the perturbation equations. Objectives: Resolving the S_8 clustering crisis by treating the dark sector as a responding medium. Key Resolutions The Hubble Tension: Re-indexed as a local material elastic limit (8.6% split) arising from environmental stiffness (\kappa). The Clustering Crisis: Resolved via a retarded stress response that reduces the S_8 tension to within \sim 1.4\sigma in mock analyses. The 15.6 Mpc Scale: Identified as an emergent characteristic resonance (k_*) of the viscoelastic web, consistent with the irregular, brain-like morphology of the large-scale structure. Project Status This repository contains the Revision 3 Legacy Treatise (historical development) and the Revision 4.0 UMC Manuscript (live numerical spec), along with implementation protocols for Boltzmann solvers such as CLASS. [e-mail]