\label{def:tau-admissible-fluid-data}
A \emph{$\tau$-admissible fluid datum} at primorial depth $k$ is a triple $\mathfrak{u}_k = (U_k, \, \phi_k, \, \mathfrak{b}_k)$ where:
\begin{enumerate}[(i)]
\item $U_k$ is a finite union of clopen cylinders in $\tau^3$ at level $\mathrm{Prim}(k)$ (Definition~\ref{def:clopen-cylinder-domain});
\item $\phi_k \colon U_k \to \widehat{\Z}_\tau[\jj]$ is an $\omega$-germ assignment: for each cylinder $C \subseteq U_k$, the restriction $\phi_k|_C$ is a section of the sheaf $\mathcal{O}(\tau^3_{\le k})$, i.e., a holomorphic function at primorial depth~$k$;
\item $\mathfrak{b}_k$ is the ABCD extraction of $\phi_k$: the four components $(A_k, B_k, C_k, D_k)$ obtained by projecting $\phi_k$ through the idempotent decomposition
\begin{equation}
\phi_k \;=\; e_+ \cdot \phi_k^{(+)} + e_- \cdot \phi_k^{(-)},
\qquad
e_\pm = \frac{1 \pm \jj}{2},
\label{eq:ch34-idempotent-decomposition}
\end{equation}
where $\phi_k^{(\pm)}$ each admit a further $(A,D)$ vs.\ $(B,C)$ sector decomposition from the 4+1 structure (Definition~\ref{def:four-plus-one-decomposition}, Ch.~10);
\item the ABCD extraction $\mathfrak{b}_k$ is \emph{bounded}: each component satisfies a primorial-level norm bound
\begin{equation}
\|X_k\|_{\mathrm{Prim}(k)} \;\le\; M \cdot \mathrm{Prim}(k)^{1/2},
\qquad X \in \{A, B, C, D\},
\label{eq:ch34-abcd-bound}
\end{equation}
for a uniform constant $M$ independent of $k$.
\end{enumerate}