Cascade Resonance Theory (KRT): Parameter-Free Geometrization of Fundamental Constants and the Dark Sector via 5D Lattice Dynamics

This publication represents the fundamental, mathematically sealed, and final formulation of the Cascade Resonance Theory (KRT). This framework breaks radically with the inductive empiricism and statistical curve-fitting of modern Standard Models. Instead, it establishes a closed, strictly deductive, and parameter-free axiomatic system that describes the vacuum as a discrete, clocked 5D bulk-lattice (L_KRT). By anchoring the mathematical structure exclusively to the exact metrological SI constants c (speed of light) and h (Planck constant), this work achieves a complete ab-initio derivation of fundamental constants (l_P, t_P, G, α⁻¹, e, k_B, m_e, m_μ) as pure hardware specifications of the cosmic grid. IMPORTANT NOTICE REGARDING PUBLICATION HISTORY: This standalone document supersedes and fundamentally reconceptualizes earlier preprints (specifically DOI: 10.5281/zenodo.18461793). All semi-empirical correction factors utilized in previous iterations have been rigorously eliminated. The deviation of the fine-structure constant is now derived entirely through transversal grid-slip (δ_Slip) and the thermal hardware noise of the measurement plane (entropic phase-jitter δ_Jitter). Consequently, earlier preprints should be considered formally deprecated and superseded by this mathematically convergent framework. Key Breakthroughs of this Paper: The Sealing of G and α⁻¹: The inverse fine-structure constant is derived from the topological degrees of freedom of the 5D grid (Φ_Geo = 138) minus geometric and entropic friction, achieving absolute numerical convergence with the experimental CODATA-2022 value. The Gravitational Constant G is deduced as the finite bulk shear modulus via a convergent impedance series. Geometric Dissolution of the Dark Sector: We demonstrate that Dark Matter is a non-material metric boundary layer of the dimensional transmission operator (T = 0.6), while Dark Energy is exposed as a pure coordinate-based volumetric dilation pressure (d³ ≈ 1.076394). Deterministic Prediction of the Muon g-2 Anomaly: The subatomic deviation is explained not by infinite QED loop corrections, but as a macroscopic quantization slip (ε ≈ 0.001222) arising during translation through the discrete lattice network. Abstract: We present the Cascade Resonance Theory (KRT), a strictly deductive geometric framework unifying localized particle mechanics with macroscopic cosmology by modeling the vacuum as a discrete, clocked 5D bulk-lattice (L_KRT). Operating as a closed axiomatic system, KRT derives the fundamental Lagrangian (L_KRT) without empirical parameter fitting. By anchoring the dimensionless 5D grid exclusively to the exact metrological constants c and h, KRT translates continuous field approximations into discrete hardware specifications, achieving an exact, parameter-free derivation of physical constants. We demonstrate that Dark Matter and Dark Energy are emergent artifacts of 5D-to-3D projections (T = 0.6, d³), effectively dissolving the dark sector. Furthermore, formalizing the quantization slip (ε) and localized entropic phase noise natively predicts the Muon g-2 deviation and the exact fine-structure constant convergence as deterministic artifacts of 5D grid geometry.