The Law of Information Saturation: Thermodynamic Inconsistency of the Continuum (C∞) and Resolution of the Gödel-Stokes Paradox

This paper demonstrates that the structural stability of physical systems requires finite limits on energy density and information processing. We identify the 'Map-Territory Confound' as the central logical flaw in contemporary theoretical physics, proving that the continuous model (C∞) fundamentally violates Einstein’s mass-energy equivalence (E=mc²) by demanding infinite mass densities . We present the Law of Information Saturation, governed by the Hernández-Valdivia Limit (εHV), as the thermodynamic safety factor that prevents systemic collapse. By formulating a modified Kogut-Susskind Hamiltonian over a $SU(3)$ simplicial lattice, we resolve the Navier-Stokes singularities and the Yang-Mills Mass Gap, proving that the universe operates as a logically consistent finite-state machine.