Fractal Riemann Hypothesis PART D: A Unified Proof of the Fractal Riemann Hypothesis Based on the Multidimensional Framework of Fractal Geometry, Quantum Field Theory, and Noncommutative Geometry

This paper proposes a multidimensional theoretical framework that rigorouslyproves that the non-trivial zeros of the fractal Zeta function lie on the critical lineRe(s) = DH2(where DH is the fractal dimension) by integrating fractal geometry,quantum field theory, noncommutative geometry, and topological quantum fieldtheory. First, based on complex analysis and group theory, we analyze the analyticcontinuation and symmetry of the fractal Zeta function. Secondly, we introducesupersymmetry algebra and renormalization group equations to explore the effectsof quantum field theory on the distribution of zeros. Furthermore, by combiningnoncommutative geometry with the topological invariants of fractal manifolds, wereveal the deep connection between the self-similarity of fractal structures and thetopological phase transitions of quantum field theory. Numerical simulations (in?cluding Monte Carlo methods, supersymmetric Hamiltonian diagonalization, topo?logical quantum computing, and tensor network algorithms) verify the theoreticalpredictions: the non-trivial zeros of the fractal Zeta function are strictly locatedon the critical line Re(s) = DH2, and non-perturbative corrections from the renor?malization group flow further suppress deviations of the zeros. This study notonly provides multidimensional theoretical support for the proof of the Fractal Rie?mann Hypothesis but also lays the foundation for fractal quantum field theory andquantum gravity theories in fractal spacetime