Dimension Engineering: The Cross-Frontier of Geometric Dimension Control and Physical Property Design

Dimension engineering offers a new paradigm for innovating material propertiesand physical laws by actively regulating the geometric dimensions and topologicalconfigurations of matter and space. This paper proposes a systematic theoreticalframework that transforms Hausdorff dimension theory, the compactification mech?anism in string theory, and dimensional regularization methods from quantum fieldtheory into actionable engineering design principles. Experimental validation cases,such as fractal catalytic materials (DH = 2.58, ethylene hydrogenation efficiencyimprovement of 42.3 ± 1.7%), topological photonic crystals (transmission loss ¡0.45dB/cm in the 1.2–1.6 µm wavelength range), and hyperdimensional computing chips(training time for four-dimensional tensor networks reduced by 31.5%), prove theuniversality of dimension optimization techniques. The research further establishesa multi-level development roadmap encompassing manufacturing processes, verifi?cation systems, and ethical governance, laying the foundation for the disciplinarydevelopment of dimension engineering.