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\label{def:e3-layer}
\begin{equation}\label{eq:ch05-e3}
    \Elayer{3} \;=\;
    \bigl(\,
        \text{observers},\;
        \text{self-model consistency},\;
        \text{interpretation},\;
        \text{self-awareness capacity}
    \,\bigr).
\end{equation}
\begin{enumerate}
    \item \textbf{Carrier} $=$ observers:
          self-referential codes ($\Elayer{2}$-admissible)
          that model their own observation.
          The object contains a model of the decoding process,
          including a representation of itself as the decoding agent.
          Error-correction capacity from $\Elayer{2}$
          provides the robustness needed for self-modelling.

    \item \textbf{Predicate} $=$ self-model consistency.
          The model's predictions about the observer's behaviour
          agree with actual behaviour
          (within $\Elayer{2}$-inherited tolerance).
          Categorical abstraction of rational agency.

    \item \textbf{Decoder} $=$ interpretation:
          from structure to meaning.
          The $\Elayer{3}$-decoder reads
          not just the code but the \emph{meaning} of the code.

    \item \textbf{Invariant} $=$ self-awareness capacity.
          The terminal invariant: there is no $\Elayer{4}$.
          The Canonical Ladder Theorem guarantees saturation.
\end{enumerate}