\label{def:proto-code}
An $\Elayer{1}$-object $X \in \operatorname{Cat}_{\T}(\Elayer{1})$ is a
\emph{proto-code} if it satisfies properties (PC1), (PC2), and (PC3) above.
Explicitly:
\begin{enumerate}
\item[(PC1)] There exists $k_0 \in \mathbb{N}$ such that $\operatorname{NF}(X)$
stabilizes at primorial depth~$k_0$, i.e.,
\begin{equation}
\operatorname{NF}(X)_k = \operatorname{NF}(X)_{k_0}
\quad \text{for all } k \geq k_0.
\label{eq:ch46-discrete-carrier}
\end{equation}

\item[(PC2)] The sector admissibility predicate
$\operatorname{Adm}_S(X) \in \{0,1\}$ for each sector
$S \in \{A, B, C, D, \omega\}$ is computable from the ABCD coordinates of $X$
at depth~$k_0$:
\begin{equation}
\operatorname{Adm}_S(X) = \operatorname{Adm}_S\bigl(A_{k_0}(X),\,
B_{k_0}(X),\, C_{k_0}(X),\, D_{k_0}(X)\bigr).
\label{eq:ch46-self-verification}
\end{equation}

\item[(PC3)] For any other $\Elayer{1}$-object $Y \neq X$, the object $X$
provides no morphism $X \to \operatorname{Adm}(Y)$: there is no internal
mechanism in $X$ that evaluates $\operatorname{Adm}_S(Y)$.
\end{enumerate}
We write $\operatorname{Proto}(\Elayer{1})$ for the full subcategory of
$\operatorname{Cat}_{\T}(\Elayer{1})$ whose objects are proto-codes.  The
morphisms in $\operatorname{Proto}(\Elayer{1})$ are tower-coherent maps that
preserve all three properties.