%
\label{def:e1-export}
%   II.D63, II.D64, II.D65, II.R22, I.D82
The \textbf{$E_1$ Export Package} is the complete collection
of structures that Book~II delivers to Book~III.
It consists of eight layers:
\begin{enumerate}
    \item[\textup{(E1.1)}]
          \textbf{Categorical structure.}
          The fibered product
          $\tau^3 = \tau^1 \times_f T^2$
          with ABCD chart (I.D17),
          fibration structure (II.T03),
          and categoricity (II.T41):
          the moduli space is a single point.

    \item[\textup{(E1.2)}]
          \textbf{Holomorphic structure.}
          The Central Theorem
          $\mathcal{O}(\tau^3) \cong A_{\mathrm{spec}}(\Lemniscate)$
          (II.T40),
          sheaf coherence (II.T32),
          the Code/Decode bijection (II.T35),
          and the 5-way Mutual Determination (II.T27).

    \item[\textup{(E1.3)}]
          \textbf{Self-enrichment.}
          Hom objects as $\tau$-objects (II.D53--D54),
          the Yoneda embedding (II.T36),
          2-categorical structure (II.D55--D56),
          and the $E_0 \to E_1$ transition (II.D58).
          This is the \textbf{$E_1$ layer}:
          $\tau$ describes its own morphisms.

    \item[\textup{(E1.4)}]
          \textbf{Numerical calibration.}
          The constants $\pi$, $e$, $\jj$, $\iota_\tau = 2/(\pi + e)$
          --- earned with their standard numerical values
          (II.T21--T24).
          Every spectral coefficient,
          every coupling constant,
          every regularity bound in Book~III
          inherits this calibration.

    \item[\textup{(E1.5)}]
          \textbf{Bipolar decomposition.}
          Every structure splits via
          $e_\pm = (1 \pm \jj)/2$:
          functions, sheaves, Hom objects,
          morphism spaces.
          The B-channel ($e_+$) and C-channel ($e_-$)
          carry independent information.
          This is the split-complex analogue
          of real and imaginary parts in classical analysis,
          but with $\jj^2 = +1$ (wave-type, not Laplacian).

    \item[\textup{(E1.6)}]
          \textbf{Regularity theory.}
          Positive regularity (II.D49):
          existence of stabilized $\omega$-germs.
          The idempotent characterization
          (II.L07, II.T32):
          holomorphic $\Leftrightarrow$ idempotent-supported.
          The 3-lemma chain
          (II.L08--L10).

    \item[\textup{(E1.7)}]
          \textbf{Manifold layer.}
          The $\tau$-manifold $(M, \mathcal{A}_\tau)$ (II.D63)
          with $\tau$-analytic atlas (II.D64),
          the exterior derivative $d_\tau$ with $d_\tau^2 = 0$ (II.D65),
          and the model spaces
          $\tau^1$ (base), $T^2$ (fiber), $\tau^3$ (total).

    \item[\textup{(E1.8)}]
          \textbf{Proof-theoretic layer.}
          The K5 diagonal discipline (I.X05)
          and its linear logic correspondence (I.T37):
          $\tau$'s proof theory is $!$-free linear logic.
          The Enrichment Frontier Classification (I.D82)
          maps the $E_0 \to E_1 \to E_2 \to E_3$ ladder
          onto the foundational landscape.
\end{enumerate}

\smallskip\noindent
\textbf{Notation.}
We write $\mathsf{Export}(E_1)$ for this 8-layer package,
and say that Book~III \textbf{receives} $\mathsf{Export}(E_1)$
as its starting configuration.
Book~III is not permitted to assume any structure
not contained in $\mathsf{Export}(E_1)$.