Algorithmic Resolution Optimization and Asymptotic Convergence of Remnant States within Discrete Spacetime Lattice Dynamics: Companion Manuscript III

To fundamentally regularize the thermodynamic and informational divergences inherent in continuous quantum field theory, this paper introduces a unified information-theoretic framework over a discrete spacetime lattice. First, we resolve the long-standing Tolman entropy paradox of cyclic cosmology by executing an iterative discrete recurrence relation where accumulated generational entropy functions as a dynamic feedback mechanism to self-optimize the spatial resolution scale. Second, we model the terminal phase of black hole evaporation, proving that the holographic data throttling filter regularizes the infinite Hawking temperature divergence. This process isolates a stable, quantized finite remnant preserving exactly pi nats of irreducible holographic entropy, securing strict 100% quantum unitarity.