Fractal Riemann Hypothesis PART H, Generation of Fractal Structures Based on Information-Computation Axioms and Proof of Riemann-Type Conjectures

This paper proposes a theoretical framework based on two fundamental principles of information conservation and the computability of physical processes, aimingto unify the description of the generation mechanism of fractal structures. Withinthis framework, we regard fractals as the macroscopic manifestation of an underlying, discrete, information-conserving quantum computational process. Theiterative generation process of their self-similarity is modeled as a series of ”selfreferential reconstructions” between ”semantic layers”. By demonstrating that thequantization behavior of information potential difference (quantum relative entropy) and the constraints of system symmetry within this computational process,we rigorously derive the analytic properties of a class of fractal zeta functions andprove that all their non-trivial zeros lie on the critical line Re(s) = DH/2 in thecomplex plane, where DH is the Hausdorff dimension of the fractal set. Theoretical predictions are verified by hybrid numerical algorithms targeting typical fractals (e.g., the Sierpiński carpet), with results showing that the real parts of zerosare statistically significantly clustered near the theoretically predicted value. Thisresearch establishes a self-consistent theoretical bridge between fractal geometry,quantum information, and analytic number theory.