As a core unsolved problem in analytic number theory for over a century, the Riemann Hypothesis has long been defined as a zero-distribution problem of complex analytic functions in traditional research. Conventional studies rely on complex analysis iterative deduction, numerical fitting and probabilistic statistics, yet fail to reveal the underlying coupling mechanism between prime distribution and the zeros of the ζ-function. Essentially, the Riemann Hypothesis is not merely a complex function analytic problem; it is a hierarchical steady-state phase-locking problem of the Π real-imaginary binary topological field on the complex plane. Traditional mathematics defines Π as a single transcendental constant without distinguishing its real and imaginary topological components, separating the intrinsic correlation between discrete number theory systems and continuous topological fields. This fundamental limitation prevents the axiomatic interpretation of the ordered distribution of primes and the constrained law of ζ zeros. Based on three original axioms — the 16-bit rigid real truncation axiom, the Π real-imaginary binary topological ontology axiom, and the arithmetic nested topological shell axiom — this paper constructs an innovative axiomatic system, accomplishing the mechanistic interpretation and rigorous closed-loop proof of the Riemann Hypothesis from topological essence.
xiaogang shui (Sat,) studied this question.