The Theory of Dimension-Dependent Mathematical Laws in a Fractal Number Theory Framework and Scientific Validation

This study establishes a novel axiomatic framework combining fractal geome?try and number theory, unveiling the dynamic relationship between mathematicaltools and spatial dimensions. By constructing dimension-dependent measure theoryand fractional differential equations, we have, for the first time, observed the di?mensional sensitivity of mathematical laws in an experimental system. Throughcontrolled graphene wrinkle experiments and fractal dynamics simulations, thequantitative relationship between renormalized differential operators and dimen?sional parameters was validated, offering a new empirical paradigm for foundationalmathematical research