F = f·v(Zₙ): The Equation That Replaces E = mc²

This foundational document introduces the FVZ equation — F = f · v(Zₙ) — as the primal structural law of the D10Z Mechanics of Infinity. It proposes that all physical manifestations of force, energy, and mass emerge from the interplay of frequency (f) and vibration modulated by a quantized nodal parameter (Zₙ), situated in the Spiderweb Fabric (TTAϵ), a quantum fractal mesh at scale GM = 10⁻⁵¹ m. The FVZ formulation subsumes and transcends Einstein’s E = mc², offering a deeper origin for mass, curvature, and phase. Every interaction, from cosmological expansion to subatomic decay, is recast as a nodal resonance process governed by this law. This document sets the ontological base for the D10Z system, including: Derivation of FVZ from TTA nodal interactions Structural definition of the Zₙ parameter as an activation scalar for coherence Applications in cosmology, particle physics, quantum computation, and DNA resonance Theoretical and numerical validation over 2000 simulations Keywords:D10Z, FVZ Law, f·v(Zₙ), Spiderweb Fabric, GM scale, Resonance, Coherence, Fundamental Force, Mass Generation, Phase Mechanics