4-D Coupled Unified Model (Final Version 6.4)

Starting from fundamental mathematical operations, this paper abandons traditional empirical symbolic systems and culturally dependent interpretations. With 1⁰ as the generative primitive, 1 and division as evolutionary rules, and 0 as logical isolation and the vacuum boundary, a four-dimensional entity necessarily emerges under constraints of structural stability. Through the mechanism of holistic four-dimensional coexistence, the core structure of three coupled standard 4D units ₄F is coherently derived: ₄F + ₄F + ₄F = 12, establishing a novel twelve-order 4D coupled scaling system. The model takes the form of a closed Pythagorean circular truncated cone, with a single 4D double-cone core performing staggered motion in three sequential phases, appearing as three coordinated cones while remaining fundamentally one unified structure. This model achieves a unified explanation of the eight core cosmic problems using only three sets of four-dimensional units coupled into a twelve-order scaling system. Higher dimensions and additional four-dimensional structures can be regarded as natural extensions of this framework with consistent underlying laws, so that a unified description can be achieved without redundant dimensions. Independent of traditional numerical symbolism, this model focuses on constructing the next-generation scientific experimental platform with strong constructiveness and practicality, supporting independent partition tests and joint comprehensive verification. Based on the twelve-order scale and four-dimensional coupling mechanism, it provides a rigorously self-consistent, computable, experimentally feasible and extensible theoretical foundation and engineering implementation path for research in aerospace engineering, advanced materials, coupled torsion control, field dynamic equilibrium, high-dimensional information transmission and novel field physics.