Thermodynamic Origin of Time and Cosmic Evolution: The Lattice Crystallization Model

This paper concludes the EMU pentalogy by addressing the origin of the vacuum lattice itself and the thermodynamic arrow of time. We propose that the Big Bang was not a singularity, but a **cosmological phase transition** where a primordial superfluid scalar field crystallized into the discrete lattice Z3. We identify Cosmic Inflation with the rapid expansion driven by the **latent heat of vacuum crystallization**. Furthermore, we define "Time" not as a fundamental dimension, but as the irreversible accumulation of **topological entanglement entropy** among lattice defects. This framework replaces the "Heat Death" scenario with a "Topological Saturation" limit, unifying cosmology with the discrete mechanics of the vacuum.