Paper I Axiom System and Intrinsic Properties of Spatial Granularity

This is Paper I of the Planck Deformation Unit Space Theory (PDUST) series. It establishes the complete axiomatic foundation of the theory. The five axioms are proposed and formulated mathematically: - Axiom 1 (Spatial Structure): Space is continuous with intrinsic energy density ρ₀; deformation has ℓₚ₀³ as the minimum definable volume - Axiom 2 (Space String): Boundaries between deformation units are purely geometric, with no physical properties - Axiom 3 (Deformation Unit Properties): Each unit possesses elasticity, stiffness, damping, and equilibrium tendency - Axiom 4 (Equilibrium Tendency): All forces originate from the units' tendency to return to equilibrium - Axiom 5 (Particle Axiom): Particles are self-sustaining rotational configurations of space deformation units The intrinsic physical parameters of the deformation unit — geometric, elastic, rigidity, damping, and limit properties — are calculated from first principles or estimated via dimensional analysis. This axiomatic system provides the foundational framework for subsequent derivations of charge, electromagnetism, gravity, light, quantum phenomena, relativistic effects, inertia, dark matter, and cosmology in Papers II–IX.