Axioms of Spiral-Dimensional Topological Primitive and Dimensional Attenuation Law: Unification of Fundamental Physical Constants and Origin of Strengths of Five Fundamental Interactions

Modern physics faces three major fundamental challenges. First, all fundamental physical constants are determined experimentally and lack a first-principles geometric origin. Second, the Standard Model and General Relativity are theoretically disconnected, failing to unify all fundamental interactions. Third, quantum systems and gravitational systems cannot be reconciled at the fundamental level. To address these issues, this paper establishes an axiomatic system for the unified spiral-dimensional theory. We define the spiral topological primitive, the indivisible minimum topological unit of the universe. The speed of light, Planck length, Planck time, Planck constant and elementary charge are all defined as inherent geometric and dynamic characteristics of the primitive’s intrinsic rotation. This paper further proposes the universal primordial spiral field originating from the cosmic primordial black hole. As the minimum quantum unit of the universe, all spiral primitives exist universally attached to the primordial spiral field, laying a fundamental foundation for the unification of quantum and gravitational systems. Based on the topological evolution mechanism of hierarchical spiral nesting, closed projection and dimensional reduction, we formulate the fundamental law of spiral-dimensional attenuation and determine the intrinsic single-stage topological attenuation factor \ (e^-2\). Combined with the topological effect of bidirectional symmetric coupling of electromagnetic interactions, the fine-structure constant is derived from first principles. Under the zero-order dominant approximation, a reasonable relative error of 2. 36% exists between the theoretical result and experimental data. This deviation arises from the truncation of high-order nesting effects and dimensional projection corrections, and does not invalidate the core mechanism. Using the above theoretical framework, we analytically derive the vacuum permittivity, vacuum permeability and universal gravitational constant, forming a self-consistent closed system of all fundamental physical constants. We introduce the master equation of the unified spiral field and classify five fundamental interactions by their corresponding spiral dimensional hierarchies. Combined with the dimensional attenuation law and electromagnetic coupling correction, the theoretical strength ratios of the five interactions are calculated, which are highly consistent with the orders of magnitude observed in experiments. This work constructs a self-contained fundamental physical axiom system featuring pure geometric topology, no free parameters, and the inherent unity of quantum mechanics and gravity. It provides a new theoretical paradigm for the development of the grand unified field theory and the integration of quantum gravity.