First-Principles Derivation of the Fine-Structure Constant in the Helical Dimension Theory

Traditional physical theories struggle to analytically derive the fine-structure constant from first principles, nor can they effectively unify quantum mechanics with general relativity or achieve a homologous description of fundamental interactions. This paper abandons the assumption of flat space, establishes an axiomatic system of helically nested dimensional topology, and derives the law of dimensional attenuation. By mapping zero-dimensional primitives to the strong interaction and first-order helices to the electromagnetic interaction, combined with the geometric gain of dual topological structures, the fine-structure constant is analytically obtained. The relative error between the theoretical value and the CODATA experimental value is 2.36%, which arises because the first-order model does not incorporate higher-order effects such as the global topological field and helical axial precession. Based on the unified rule of dimensional attenuation, this paper successively derives the vacuum permittivity, vacuum permeability, and gravitational constant, establishes a topological correlation between the strong and electromagnetic interactions via the fine-structure constant, and reveals the intrinsic link between the electromagnetic and gravitational interactions via the gravitational constant, initially realizing the unification of three fundamental interactions and laying the foundation for constructing a unified field theory encompassing all four fundamental interactions. In accordance with the continuous hierarchical characteristics of helical dimensions, this theory predicts the existence of a fifth fundamental interaction in the mesoscopic regime. Combined with lattice topology and the laws of electronic helical motion, a topological design strategy for room-temperature superconducting materials is further proposed. The research demonstrates that the helical topological system has the potential to unify fundamental physical laws from the underlying geometry and guide the design of new condensed matter materials, with theoretical results available for subsequent experimental verification and theoretical refinement. Keywords: helical topology; nested dimension; dimensional attenuation; fine-structure constant; unified field theory; fifth interaction; room-temperature superconductivity