\label{prop:three-condition-sufficiency}
Let $f$ be $\tau$-admissible fluid data on a clopen cylinder domain $U \subset \tau^3$. Suppose the following three conditions hold:
\begin{enumerate}
\item[\emph{(C1)}] \textbf{Clopen locality.} The domain $U$ is a finite union of clopen cylinders at each primorial depth (Definition~\ref{def:clopen-cylinder-domain}, Ch.~34), and the Boolean cylinder algebra is closed under intersection, union, and complement.

\item[\emph{(C2)}] \textbf{$\omega$-Germ determinacy.} At each primorial level $\operatorname{Prim}(n)$, the Local Hartogs continuation $\operatorname{Ext}_n$ produces a unique extension of the boundary data into the interior of~$U_n$ (Theorem~\ref{thm:hartogs-flow-theorem}(i), Ch.~36). There is no freedom in the evolved data: it is \emph{forced} by the boundary assignment.

\item[\emph{(C3)}] \textbf{Defect-horizon contractivity.} The defect functional $\Delta(f, n)$ (Definition~\ref{def:defect-functional}, Ch.~35) satisfies $\Delta(f, n{+}1) \leq \kappa \cdot \Delta(f, n)$ for all $n$ sufficiently large, with $\kappa < 1$ (Proposition~\ref{prop:defect-contractivity}, Ch.~35).
\end{enumerate}
Then $H_{\mathrm{flow}}(f)$ admits a stabilized $\omega$-germ at every point $x \in U$.