Unified Geometric Mechanics of Space Lattice

ABSTRACT This paper presents a unified geometric and mechanical framework describing physical interactions across quantum, molecular, planetary, and cosmic scales without relying on mass as a primary fundamental entity. Instead, all physical objects are modeled as elastic deformations (indentations equal to the Schwarzschild radius, Rs) within a tensioned space-time lattice characterized by universal stiffness (6.732955 * 10^26 kg/m), vacuum elasticity (6.674300 * 10^-11 m^3/(kg*s^2)), and lattice tension force (1.210256 * 10^44 N). Using standard arithmetic calculations, we derive the Force Passports of the Sun, Earth, electron, and proton, introducing a dimensionless quantum scale switch (4.1657 * 10^36) and the Nuclear Reductor invariant (6150) that yields the universal nucleon assembly step (1.670 - 1.672 fm). Furthermore, we reformulate the Ideal Gas Law (Mendeleev-Clapeyron equation) and barometric relations into pure geometric expressions of planetary and atmospheric indentations. The model reproduces surface pressures, temperatures, molar concentrations, densities, and sound speeds for Earth, Mars, Venus, and Titan with 94% to 99.9% accuracy. We also derive planetary magnetic field strengths and magnetospheric compression thresholds during geomagnetic storms, formulate the Root Law of Vortex Decay (4.5 billion km at 5.4 km/s to 18 billion km at 2.7 km/s, terminating at 1.1 trillion km), propose a testable hypothesis on interstellar cell compression (~18.75x - 19.7x), and provide a blind predictive profile for the exoplanet TRAPPIST-1e ahead of definitive JWST atmospheric measurements.