Thermodynamics of the Vacuum Lattice: From Black Hole Entropy to Cosmological Latent Heat

In Lattice-Continuous Monism (LCM), entropy is not merely a statistical measure ofdisorder but a physical quantity defining the phase state of the vacuum energy. This paper summarizes the thermodynamic structure of the LCM universe, treating the vacuum asa hyper-rigid medium undergoing phase transitions. We present the geometric derivationof the Bekenstein-Hawking entropy (SBH) by reinterpreting the event horizon as a latticemelting front. Furthermore, we define the ”Big Bang” not as a singularity but as a crystallization process releasing latent heat (2.24%), which resolves the cosmological lithiumproblem. Finally, we address the Information Paradox through the lens of topological knotdissolution in a superfluid interior.