The Information Matter Unified Field Theory A Complete Geometric Physical Synthesis

This paper completes the three part series establishing the ``information = matter'' unified theory. Paper A developed the geometric foundations and derived the information–Einstein equation. Paper B demonstrated that quantum field theoryemerges naturally from information geometry. The present work synthesizes these results into a single unified field theory, deriving all necessary structural equations, conservation laws, coupling rules, and physical predictions. We construct a unified action functional whose variations yield: (i) the classical information–Einstein equation, (ii) the quantum information–Einstein equation, (iii) the unified information–matter coupling equation, (iv) the information–Yang–Mills equation, (v) the information–Dirac equation, (vi) the unified continuity equation, and (vii) the master renormalization flow. All derivations are explicit and rigorous. Several new original equations (1–12) are introduced, representing the final structural backbone of the unified theory.