Thermodynamic Decoupling at the Planck Boundary: The t=0 Non-Thermal Pure State Blueprint

This paper challenges the prevailing assumption of a "Hot Singularity" in standard cosmology by rigorously re-evaluating the physical properties of the universe at the exact coordinate of t=0. Relying on canonical quantum mechanics and statistical thermodynamics, we argue that the extrapolation of infinite temperature toward the Planck Scale suffers from epistemic overreach. At the boundary of t=0, as demonstrated by the Wheeler-DeWitt equation, the system loses its time evolution parameter (dt=0). In the framework of statistical mechanics, the absence of time halts all kinetic dynamics and particle motion. Consequently, kinetic energy collapses to zero, necessitating a state of static equilibrium at absolute zero temperature, which we term the "Cool Birth." We further define this initial condition as a Pure State with zero von Neumann entropy, conceptualizing the t=0 boundary not as a boiling plasma, but as a pure quantum information blueprint. To maintain rigorous logical deduction, this paper strictly isolates its scope to the physical conditions precisely at t=0, deliberately excluding any discussion regarding the causal origins of this boundary or the subsequent dynamic mechanisms of cosmic inflation.