Entropy

We present a thermodynamic analysis of the Topological Lagrangian Model, characterizing the Mk4 Hyperbottle manifold as a non-orientable closed system where celestial poles function as recursive entropic filters.We derive the Metric Tension (PULL) as a function of vacuum coherence and identify the arrow of time with the relaxation of geometric shear stress from the high-pressure intake to the relaxed exhaust.This pressure differential drives the refinement of the vacuum, yielding a calculated refinement efficiency of approximately 7.2%.We further demonstrate that the expansion of space constitutes the venting of entropic waste, resolving the Hubble tension through a derived topological scalar Λ t .Finally, we identify the dark matter halo as the gravitational wake of metric energy tunneling into the manifold's foundation layers, consistent with the instanton suppression rates of the phase-loop criterion.