THE GEOMETRIC ORIGIN OF GRAVITY S₀ = 1 / (μ₀ ε₀)

1. Introduction Gravity is weaker than electromagnetism by a factor of approximately 10⁴². Traditional physics treats G as a fundamental constant, providing no explanation for this hierarchy. We introduce the Stiffness Hypothesis: > Gravity is the diluted geometric response of vacuum stiffness when mass-energy couples to a discrete information grid. We adopt an inverted metrological approach: Standard approach: Planck length is defined using G. Our approach: The minimum vacuum length lₘᵢₙ is fundamental, and G is derived from it. 2. Derivation Framework We proceed through five steps: 1. Vacuum stiffness S₀ 2. Electron interaction horizon rₑ 3. Vacuum information grain lₘᵢₙ 4. Geometric damping factor ℕ 5. Derived gravitational constant G