%
\label{def:e0-e1-transition}
The \textbf{$\Estage{0}/\Estage{1}$ transition}
is the passage from the structural content
of~$\Estage{0}$ (Groups~A--D above)
to the enriched content of~$\Estage{1}$:

\medskip
\begin{center}
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\begin{tabular}{@{}p{0.15\linewidth} p{0.38\linewidth} p{0.38\linewidth}@{}}
\hline
& \textbf{$\Estage{0}$} & \textbf{$\Estage{1}$} \\
\hline
\textit{Objects}
    & Finite and profinite elements of~$\T$
    & Same, plus $\Hom(A,B)$ as objects \\
\textit{Morphisms}
    & $\omega$-germ transformers
    & Same, plus 2-morphisms between Hom objects \\
\textit{Holomorphy}
    & Boundary characters; Global Hartogs
    & Interior holomorphy; Central Theorem \\
\textit{Constants}
    & $\iota_\tau$ (algebraic), $\pi$, $e$ (earned)
    & Same, now with geometric confirmation \\
\textit{Coordinate data}
    & ABCD chart $\Phi(x)$
    & Same, extended to $\tau^3$ fibration \\
\textit{Self-reference}
    & None
    & $\T$ enriches over itself; Yoneda \\
\textit{Categoricity}
    & Unique normal form (NF)
    & Unique category ($\tau^3$ discovered, not constructed) \\
\hline
\end{tabular}
\end{center}

\medskip\noindent
The transition is characterized by a single structural fact:
\[
    \boxed{%
    \text{At } \Estage{0},\;
    \Hom(A,B) \text{ is an external set.}
    \quad
    \text{At } \Estage{1},\;
    \Hom(A,B) \in \Obj(\T).}
\]
This internalization is what enables the Yoneda embedding (II.T36),
which in turn enables the Central Theorem (II.T40).