\label{def:e1-mutual-determination}
The \emph{$\Elayer{1}$ Mutual Determination instance} is the triple $(B_1, S_1, I_1)$ defined as follows.
\begin{enumerate}
\item[\emph{(B$_1$)}] \textbf{Boundary data.} $\tau$-admissible data on clopen cylinder domains at enrichment level~$\Elayer{1}$: split-complex sections $\phi^{\jj}$ satisfying bounded extraction, tower coherence, and Kirchhoff conservation.

\item[\emph{(S$_1$)}] \textbf{Spectral structure.} The sector-decomposed spectral algebra $A_{\mathrm{spec}}(\Lemniscate) \otimes R_n^{\jj}$, equipped with the defect functional $\Delta$ and the sector projections $\pi_S$ for $S \in \{A, B, C, D, \omega\}$.

\item[\emph{(I$_1$)}] \textbf{Interior consequence.} The stabilized $\omega$-germ structure: at every point of the clopen cylinder domain, the $\omega$-germ of the Hartogs flow stabilizes at finite primorial depth with sector-wise NF-addressable canonical form and positive spectral gap in the strong sector.
\end{enumerate}
The three components satisfy full bidirectionality:
\begin{equation}
B_1 \;\longleftrightarrow\; S_1 \;\longleftrightarrow\; I_1.
\label{eq:ch44-mutual-determination-e1}
\end{equation}
The forward direction ($B_1 \to S_1 \to I_1$) is the content of Part~V's proofs. The backward direction ($I_1 \to S_1 \to B_1$) holds because each interior consequence reconstructs its spectral invariants (stabilized germs determine defect values; gap existence determines NF lattice structure; addressability determines balanced spectral content), and the spectral invariants reconstruct the boundary data via the primorial tower maps.