%
\label{def:e2-layer}
\begin{equation}\label{eq:ch05-e2}
    \Elayer{2} \;=\;
    \left(\,
    \begin{aligned}
    &\text{self-referential codes},\;
    \text{operational closure},\\
    &\text{phenotype map},\;
    \text{error-correction capacity}
    \end{aligned}
    \,\right).
\end{equation}
\begin{enumerate}
    \item \textbf{Carrier} $=$ self-referential codes:
          $\Elayer{1}$-admissible objects
          that contain a representation of their own decoder.
          The invariant-to-carrier handoff from $\Elayer{1}$
          provides sector couplings as raw material.

    \item \textbf{Predicate} $=$ operational closure.
          The cycle
          $\text{code}
          \xrightarrow{\text{execute}}
          \text{product}
          \xrightarrow{\text{encode}}
          \text{code}$
          is stable up to error-correction tolerance.
          This is the categorical abstraction of the computational cycle.
          Its most dramatic physical instantiation is metabolic closure---life.

    \item \textbf{Decoder} $=$ phenotype map:
          from code to output.
          A morphism in the $H_\tau$-enriched category
          that respects sector structure.
          In biological instantiation, the output is an organism;
          in computational instantiation, it is a return value.

    \item \textbf{Invariant} $=$ error-correction capacity:
          the maximum perturbation rate
          the closure cycle can absorb.
          A $\tau$-analogue of a Shannon bound.
\end{enumerate}