Fractal Riemann Hypothesis. PART B Fractal Geometry and Quantum Entanglement Entropy: A Novel Perspective and Rigorous Proof of the Fractal Riemann Hypothesis.

his paper presents a novel theoretical framework based on quantum entangle?ment entropy and fractal geometry, rigorously proving that the non-trivial zerosof the fractal Zeta function lie on the critical line Re(s) = DH/2 (where DH isthe fractal dimension). By defining quantum entangled states on fractal manifolds,we reveal the deep connection between the scaling law of entanglement entropyand the distribution of Zeta function zeros. Theoretical derivations show that theself-similarity of fractal structures constrains the zero positions through the globalcorrelations of quantum entanglement. Combining conformal field theory and non?perturbative renormalization group analysis, we further suppress the possibility ofzeros deviating from the critical line. Numerically, quantum Monte Carlo and ten?sor network algorithms are used to simulate the Sierpi´nski carpet (DH = log3),with results showing that the zero density peaks near Re(s) = 0.792 (error ¡ 2%),consistent with theoretical predictions. This study not only provides a new proofpath for the Fractal Riemann Hypothesis but also lays the foundation for quantuminformation theory in fractal spacetime