Paper I Axiom System and Intrinsic Properties of Spatial Granularity

This paper is the first in the Planck Cube Space Theory series. It establishes the complete axiomatic foundation of the theory, including the discrete structure of space (Planck cubes), the intrinsic properties of each cube (elasticity, stiffness, damping, bidirectional equilibrium tendencies), the force laws derived from the equilibrium tendency, and the definition of a particle as a spinning energy bundle. All geometric, elastic, stiffness, damping, saturation, and restoration parameters of the Planck cube are derived or estimated from first principles. The axiomatic system provides the foundational framework for subsequent derivations of charge quantization, gravity, the nature of light, quantum phenomena, relativistic effects, inertia, dark matter, and cosmology.