Phantom-Net: The Coherence Engine - Core Documentation Release 2025

AbstractThe Phantom-Net (PN) framework proposes a unified physical model where fundamental interactions emerge from a continuous substrate characterized by density (ρ) and stiffness (K) fields. The dynamics are governed by the wave equation:ρ ∂²Ψ/∂t² = K ∇²Ψ − α|Ψ|²Ψ − β ∇²(|∇Ψ|²) − γ ⟨|Ψ|²⟩Ψ.This work establishes: (1) mathematical foundations connecting classical, quantum, and relativistic phenomena through substrate coherence; (2) numerical implementation protocols ensuring computational verifiability; (3) experimental validation criteria with quantitative falsification thresholds. The framework demonstrates empirical correspondence in gravitational lensing (±1%), quantum phase coherence (±2%), and energy conservation (ΔE/E₀ < 10⁻⁴), while maintaining philosophical coherence through its ethical-geometric principle. All implementations are cross-referenced with complete mathematical specifications and validation protocols.