The LCM-Vacuum Phase Equation: A Unified Hydrodynamic Approach to Spacetime, Matter, and Constants

The Standard Model of Cosmology relies on a set of independent parameters (Λ, Ωm, H0) to describe theuniverse. In this work, we explore a unified geometric framework, Lattice-Continuous Monism (LCM), whichposits that the universe evolved from a primordial liquid vacuum into a hyper-rigid truncated octahedron latticevia a crystallization phase transition. We introduce the ”LCM-Vacuum Phase Equation” as the masterequation governing this cosmogenesis. Based on this formalism, we present derivations for: (1) The speed of lightas the lattice elastic wave velocity (c = K/ρ); (2) The latent heat of the Big Bang (L ≈ 2.27%), which alignswith the energy budget required to resolve the Cosmological Lithium Problem; and (3) A fundamental defectdensity (1/14), which offers a geometric mechanism to alleviate the Hubble Tension. These results suggest thatthe fundamental constants and dynamics of the universe may be emergent properties of a crystallizing vacuum.