The Computational Unified Framework: Resolving Quantum Measurement, Cosmological Fine-Tuning, and Black Hole Horizons within the PLI Architecture

This technical treatise establishes the unified mathematical extension of the Primary Logical Infrastructure (PLI) framework (Sottosanti, 2026). By mapping the continuous spacetime manifold onto a discrete, graph-theoretical matrix (G_p), the analytical and physical breakdowns of orthodox continuous physics are systematically regularized. First, bridging the author's foundational work on syntactic expansions (ΦI → IV) to wave mechanics, this paper resolves the quantum measurement paradox by modeling wave function collapse as a bandwidth-saturation phenomenon (I ≥ C_max), leveraging spectral graph theory and Laplacian eigenvectors via the Deterministic Topological Splitting (DTS) operator. Second, it addresses the cosmological fine-tuning problem by replacing spatial multiverses with a sequential, iterative execution loop driven by a deterministic topological matrix mutation operator (Ω), ensuring macro-state invariance across cosmic resets. Third, it evaluates the interior of black holes through a localized Syntactic Deceleration function γ(r), proving that as the local informational flux approaches the capacity threshold (I(r) → C_max), the temporal step drops to absolute zero (Δτ → 0), substituting the relativistic physical singularity with a clean, sub-metric computational runtime freeze. The compilation of Addenda II, III, and IV completes the architectural extensions of the PLI, arguing that the universe can be completely and rigorously modeled as a self-contained, non-divergent computational system.