The Prime-Prime Lattice (PPL) Space and Non-Equilibrium Open Wave Dynamics: Part III: Microscopic Field Vibrations, Quantum Action from Zeta, and the Thermodynamic Origin of Three Fundamental Forces

This paper establishes the third component of the Prime-Prime Lattice (PPL) framework, unifying microscopic quantum field actions and the three fundamental interactions Coulombic, magnetic, and gravitational forces under a singular, constant-free monistic paradigm. Building upon the multiplicative vacuum infrastructure (|∅⟩=1) and macroscopic spacetime phase transitions demonstrated in Parts I and II, we derive the empirical Planck constant (h) from number-theoretic first principles. We show that the SI quantum of action arises naturally from the distribution of the native PPL link potential (h_PPL=1) across the simple cubic grid coordination channels (C_PPL=2x3=6), filtered through the four-dimensional energy density ζ(4). Furthermore, we define the fundamental field as an Euler product of local prime-dimensional phase coherence. Within this framework, mass nodes manifest as topological singularities corresponding to the non-trivial zeros of the Riemann zeta function, and the three fundamental forces emerge as autonomous optimization modes of a source-free universal wave equation whose right-hand side is identically zero (0).