Unified Theory of Membrane Spacetime — Part II: Simplicial Mechanics of the 6D Pre-Planckian Membrane, Cosmic Respiration, and the Resolution of the Cosmological Hubble Tension.

We present a non-perturbative, deterministic framework that unifies cosmic acceleration, large-scale structural distribution, and localized gravitational coupling by replacing the stochastic vacuum and dark sector paradigms with the hydrodynamic interface mechanics of the Summa Teorica. We demonstrate that what physics misinterprets as dark energy (repulsion) and dark matter (attraction) are not independent substances or orphan forces; rather, they are the two complementary metabolic phases of a single trans-membrane metric respiration cycle executed by Current I across a 6D compactified half-hexagon simplicial membrane (\(\mathcal{M}_{6D}\)) operating under a core refresh frequency of exactly \(10.00\text{ MHz}\). The cosmic web and colossal macroscopic voids are shown to be the predictable pressure topology of this six-dimensional informational fluid. Furthermore, this explicit scale-invariant mapping resolves the cosmological Hubble Tension without free empirical parameters, yielding the precise global and local eigenvalues (\(H_0^{\text{Global}} \equiv 67.423\text{ km/s/Mpc}\) and \(H_0^{\text{Local}} \equiv 72.486\text{ km/s/Mpc}\)) as a direct function of the invariant Conformal Attenuation Delta of exactly \(0.045\%\) (\(\Delta_\gamma = 0.00045\)). At the stellar infrared scale, the unified field equations match the luminosity distance curves of Type Ia Supernovae, while at the ultraviolet subatomic scale, boundary amplification tracks color confinement inside the proton. We provide the analytical framework, validation through existing data using the JANO-II radio telescope algorithm, and a definitive Python simulation mapping the non-linear inverse pressure gradients of macroscopic cosmic voids.