\label{def:strong-sector-e1}
Let $\mathcal{A}_{\mathrm{spec}}(\mathbb{L})$ be the spectral algebra on $\mathbb{L}$ and let $E_1$ denote the first enrichment level (enrichment by the $\operatorname{Prim}$-tower with split-complex coefficients). The \emph{strong sector} at $E_1$ is the full subcategory
\begin{equation}
\operatorname{Strong}_{E_1} \;\subset\; \mathcal{A}_{\mathrm{spec}}(\mathbb{L})\big|_{E_1}
\label{eq:ch38-strong-sector-def}
\end{equation}
consisting of all objects whose spectral support lies entirely in $\operatorname{Sector}(C) \subseteq \operatorname{Char}(\mathbb{L})$. Concretely, an element $g \in \operatorname{Strong}_{E_1}$ satisfies:
\begin{enumerate}[(i)]
\item $g$ is a section of the sheaf $\mathcal{O}(\tau^3_{\le k})$ for some primorial depth $k$;
\item the ABCD extraction of $g$ yields $g_A = g_B = g_D = 0$ and $g_\omega = 0$;
\item the surviving component $g_C$ is $\chi_-$-dominant: writing $g_C = e_+ \cdot g_{C,+} + e_- \cdot g_{C,-}$, the spectral mass is concentrated in $g_{C,-}$.
\end{enumerate}