Research the Natural Number System and the Riemann Hypothesis within the Framework of Fractal Number Theory

This paper constructs a novel axiomatic framework integratingfractal geometry and analytic number theory, systematically revealingthe intrinsic fractal homogeneity between the distribution of naturalnumbers and the zeros of the Riemann zeta function. Key innova?tions include the Fractal Measure Mapping Theorem, the Criti?cal Line Dynamics Model, and the Fractal Sieving Algorithm,establishing a cross-disciplinary framework for ”Fractal Number The?ory.” Through theoretical derivations, algorithmic validation, and in?terdisciplinary integration, this work provides a mathematically rig?orous and computationally feasible paradigm for addressing the Gold?bach Conjecture and the Riemann Hypothesis.