NGIFT 6.4: Non-local Gradient Informational Field Theory – Quantitative Proofs for Scale Unification across Galactic and Atomic Systems

This paper presents the finalized, quantitative framework for the Non-local Gradient Informational Field Theory (NGIFT). By replacing abstract materialist constraints with Informational Processing Density (IPD) and Matter Lag (𝜏 ) equations within a nonlocal computational substrate (The Matrix), we demonstrate absolute cross-scale unification. We provide exact numerical matches for cosmological phenomena (the Cosmic Horseshoe gravitational lens radius at 5.01") and subatomic quantum thresholds (the hydrogen ground-state energy at -13.61eV) using a single, invariant base equation of motion without any hidden or dark matter parameters 1.1.