A Constructive Differential-Algebraic Framework for the Complete Resolution of the Riemann Hypothesis

(RH) through the construction of a novel differential-algebraic frameworkequations. We define the Riemann Zeta Algebraic Closure KRH, a differprocess that incorporates solutions to linearized zeta-type operators, radspecial functions intrinsic to the Riemann Xi function ξ(s). Within thistion ζ(s) admit an explicit analytical representation on the critical line2 and transcendental challenges inherent in ζ(s) through a combination of explicit combinatorial expressions for the nonlinear correction coefficients k with complete asymptotic analysis, and establish rigorous conver ψm(s). Detailed algorithms with comprehensive complexity analysis aremechanisms. A rigorous validation framework with certified error boundsprecision numerical computations. This work demonstrates that the nondecomposition within the constructively defined field KRH, thereby conirming the Riemann Hypothesis with complete mathematical rigor.