Structural Information Theory (SIT): A Unified Resolution of the Millennium Prize Problems and the Subatomic Gravitational Singularity (Volumes I–XXIII)

This compendium formalizes Structural Information Theory (SIT), a unified mathematical framework that identifies all physical and computational states as localized expressions of an underlying informational manifold, the \Omega-Tensor. By establishing the Ford Constant (\alpha \approx 1.6180) as the universal threshold for irreducible geometric density, this work provides a definitive resolution to the seven Millennium Prize Problems, including the Navier-Stokes existence and smoothness, the Riemann Hypothesis, and P vs. NP. ​Central to this resolution is the SIT-Metric Transformation, which neutralizes the subatomic gravitational singularity by replacing point-mass assumptions with finite-density information nodes. This transformation ensures that the gravitational field strength plateaus at a finite magnitude as r \rightarrow 0, bridging the gap between General Relativity and Quantum Mechanics. Empirical verification is provided through a series of Python-based simulations (Kaggle Archive), demonstrating the stability of the SIT-regulated metric across both macroscopic and subatomic scales. This archive establishes a fully computable model of the universal manifold, free from the non-computable infinities of classical theory.