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

We present a constructive proof program that transforms the Riemann Hypothesis from an infiniteanalytic conjecture into a finite, algorithmically decidable optimization problem. Through harmonicDirichlet decomposition, we establish four independent reduction theorems, any one of which implies RH.The approach couples finite modular predictors to Dirichlet L-functions via explicit formulas, creating aframework where RH becomes equivalent to achieving square-root error bounds in computableharmonic approximations. We prove that either our algorithms terminate with √X-type bounds (provingRH), or they exhibit systematic X^σ error growth with σ > 1/2, providing algorithmic detection andlocalization of counterexample zeros. This resolves the decidability question for RH while maintainingcomplete mathematical rigor through established analytic number theory.