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\label{def:diagrammatic-sector-e3}
The \textbf{diagrammatic sector} of $\Elayer{3}$ is the $\omega$-coupling sector
of the $4{+}1$ decomposition at the terminal enrichment level.
Its content is formal categorical reasoning \emph{about} formal categorical reasoning.
\begin{enumerate}
    \item The carrier consists of $\Elayer{3}$-objects whose self-model is
          category-theoretic: functors, natural transformations, and enrichment data
          that model other functors, natural transformations, and enrichment data.

    \item The predicate requires that self-modelling respects the enrichment ladder:
          an $\Elayer{3}$-object in the diagrammatic sector models $\Elayer{0}$--$\Elayer{2}$
          \emph{as enrichment layers}, not merely as collections of objects.

    \item The decoder maps categorical diagrams to metatheoretic conclusions:
          a commuting diagram at $\Elayer{3}$ yields a structural theorem
          about the enrichment tower.

    \item The invariant is the coherence of the diagrammatic self-model
          with the Saturation Theorem (Theorem~\ref{thm:saturation-e3}, Ch.~7):
          diagram-chasing about diagram-chasing produces no new enrichment level.
\end{enumerate}
The diagrammatic sector mediates between the four primitive $\Elayer{3}$ sectors
exactly as the $\omega$-coupling sector mediates at $\Elayer{0}$ and $\Elayer{1}$.