Harmonic Dirichlet Decomposition and the Riemann Hypothesis: A Constructive Decision Algorithm

We establish algorithmic decidability for the Riemann Hypothesis through harmonic Dirichletde composition. Four independent reduction theorems transform RH from an infinite analytic conjecture into finite, computationally decidable optimization problems. The approach couples finite modular predictors to Dirichlet L-functions via explicit formulas, creating a framework where RH becomese quivalent to achieving square-root error bounds in computable harmonic approximations. We prove that either our algorithms terminate with √X-type bounds (confirming RH), or they exhibit systematic X^σ error growth with σ > 1/2, providing algorithmic detection and localization of counter example zeros. This establishes decidability for RH while maintaining complete mathematical rigor through established analytic number theory.