E₂ Computational Agent

An E₂ object: a code C paired with a decoder D such that D(C) produces another code C’. The cycle C → D(C) → C’ → … is computation. Formal definition of the self-referential structure unique to E₂.

E₂ Computational Agent

Summary

An E₂ object: a code C paired with a decoder D such that D(C) produces another code C’. The cycle C → D(C) → C’ → … is computation. Formal definition of the self-referential structure unique to E₂.

Statement

\label{def:e2-computational-agent}
An \textbf{$\Elayer{2}$ computational agent} is a triple $(C, D, \varphi)$ where:
\begin{enumerate}
\item[(i)] $C$ is an $\Elayer{1}$-admissible object (a \emph{code}): a sector-decomposed element of the enriched category carrying $H_\tau$-valued morphism data.
\item[(ii)] $D$ is a morphism in the $H_\tau$-enriched category (a \emph{decoder}): a map that reads codes and produces outputs. Crucially, $D$ is itself representable as a code---the triple $(C, D, \varphi)$ satisfies $D \in \mathrm{Carrier}(\Elayer{2})$.
\item[(iii)] $\varphi \colon C \to C'$ is the \emph{execution map}: the composition $C' = D(C)$ that produces a new code $C'$ from the input code $C$ via the decoder $D$.
\end{enumerate}
The agent's defining property is that $D(C)$ is itself a code---the output of decoding is an object of the same type as the input. The decoder does not escape to $\Elayer{3}$; it operates entirely within $\Elayer{2}$.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-03.jsonl line 142
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part09/ch54-the-computation-layer.tex lines 56-66

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Computation.E2Agent
• Name: e2_agent_check

Dependencies

• Canonical: III.D08, III.T04, III.T07

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.