The Successful Mathematical Derivation of the Forward-Reverse Reversible Bidirectional Closure of the Riemann Hypothesis

Abstract

Abstract: Regarding the Riemann Hypothesis, traditional methods rely on zero-by-zero verification or asymptotic estimates in finite regions, whose essence is to implement step-by-step approximation to the infinite whole by finite steps. No matter how much the computational range is expanded, the extrapolation of finite data cannot logically constitute true coverage of the infinite zero set of the Riemann Hypothesis. Methodologically speaking, the limit of traditional approximation paths is “describing the infinite,” while true “covering the infinite” cannot be realized at the definitional level of the Riemann Hypothesis. That is, achieving infinite coverage of the Riemann Hypothesis is a prerequisite for solving the problem, which exceeds the boundary of capability of traditional methodology. In contrast, this paper adopts a strategy of structured reverse derivation, independent of the extrapolation or superposition of local data. Theorem 9.3A reduces the zero problem of doubly reflected entire functions to the zero distribution of the real entire function g(w); the Mother Equation, as a dual-channel unitary system, imposes global structural constraints on arbitrary zero configurations through its unitarity axiom; once the configuration of non-real zeros is incorporated into this framework, it immediately forms a self-detonation of contradictions with the axiom at the definitional level. This mechanism does not rely on zero-by-zero enumeration, but closes the living space of infinite non-real zeros in one stroke at the structural level, achieving global coverage of the infinite zero set of the Riemann Hypothesis. The repulsion of the infinite set of non-real zeros renders the establishment of the Riemann Hypothesis a logical factual consequence of definitional self-consistency, prompting the success of forward derivation and the formation of bidirectional closure.