This is part I https://zenodo.org/records/16978450 This is part II https://zenodo.org/records/16978117 This is part IV https://zenodo.org/records/16978234 This is Part III [https://zenodo.org/records/16978002] This work presents a unified theory of physics based on the single principle that the universe has finite information processing capacity, Imax ≈ 10¹²² bits, currently operating at ~91% saturation. From this principle, the Lambert W function emerges as the universal regulator, eliminating infinities in quantum field theory without renormalization, explaining the observed cosmological constant Λ ≈ 10⁻¹²² (Planck units) without fine-tuning, deriving the Born rule without postulates, and identifying characteristic information-processing scales (~10³⁰·⁵ ops/s). The framework naturally explains cosmic acceleration as differential time flow, removes singularities inside black holes, and unifies quantum decoherence with cosmology. Predictions include a quantum decoherence floor, JWST “impossible” galaxy ages via an age gradient, and negative redshift drift (opposite to ΛCDM). Five independent derivations converge on the saturation index C = 0.91 ± 0.04, transforming this from speculation into a fundamental principle awaiting experimental confirmation.