The Riemann Hypothesis as a Completion-Sensitive Sentence: Dirichlet-Clause Semantics, Neutral vs. Full-Weight Completion, Arbitrary Strip Zero-Set Realization, Analytic Selection, and Gödel Constraints on Completion-Totality Theories

This paper separates two clause packages that standard analytic discourse often conflates: the \emph{Dirichlet-series clause package} for the symbol \(\zeta(\cdot)\), valid only on \(\Re(s)>1\), and the \emph{completed analytic package}, in which \(\zeta\) denotes on \(\C\setminus\{1\}\) by analytic continuation. The paper studies the first package in isolation and then analyzes the space of its possible completions. We work with an explicit base evaluator \(\EDir\) in which \(\zeta(s)\) receives a value only when \(\Re(s)>1\). On the critical strip \(0