Quantized Vacuum Geometrodynamics. Part I: Tetrahedral Planck Network, Dimensionless Elastic Moduli G and k, and Field Equation Reduction

This paper provides a definitive realization of Albert Einstein's lifelong dream of a Unified Field Theory and a comprehensive Theory of Everything. By abandoning abstract spacetime metrics and reducing physical phenomena to a deterministic, discrete tetrahedral network at the Planck scale, the model unifies gravity and electromagnetism into a single framework of vacuum elasticity. The space is structured as a crystal-like lattice composed of individual Majorana-like nodes. The author presents the exact analytical proof of the dimensionless nature of the Coulomb coefficient (k) and the Gravitational constant (G), locking their values to transcendental invariants of π and Euler's number e. A rigorous, radius-free derivation of Planck's constant (h) is given, completely eliminating artificial macroscopic SI scaling dimensions. Finally, a complete reduction of Einstein's general relativity field equations down to a pure geometric 1/3 cascading rule is performed. This reduction mathematically maps the macroscopic Titius-Bode structure of cosmic systems directly onto the microstructural elastic constraints of the quantized vacuum, fulfilling Einstein's vision of reducing all physics to pure, unbroken geometry.