Formalization of the Φ-Fold Mathematical Core: The Teorema do Universo Calcul´avel (TUC) and the Silas Scale

This manuscript introduces a unified mathematical framework for complexity management in physical and informational systems, centered on the $\Phi$-Fold theory. We present two primary breakthroughs: The Silas Dissipation Scale ($\eta_{\text{Silas}}$): A geometric refinement of the 3D Navier-Stokes equations that introduces the Golden Ratio ($\Phi$) as a regulator for energy dissipation, effectively preventing mathematical singularities in turbulent regimes. The Calculable Universe Theorem (TUC): A cybernetic model for cosmology where accelerated expansion is defined as a negative feedback response to spectral information saturation. By defining "Spectral Saturation Pressure" ($P_{\text{sat}}$), we argue that the Universe expands to maintain its dominant eigenvalue below the critical threshold of $\Phi \approx 1.618$, ensuring the preservation of causal calculability. This work bridges the gap between fluid mechanics, graph theory, and cosmology, offering testable predictions for galactic rotation curves and turbulent flow stabilization.