A Unified Structure Theory of Prime Numbers - Conceptual Framework and Fundamental Path

This paper returns to the fundamental origin of arithmetic, revealing the intrinsic constraints of prime distribution by a unified underlying structure. By combining matrix structure and numeral-system constraints, it establishes a unified closed loop connecting prime distribution, the Goldbach conjecture, and the Riemann hypothesis. This work shows that the core laws of primes can be expressed by minimal primitive rules, and complex problems admit simple, self-consistent, and complete solutions within a unified framework.