Layer Template

Each enrichment layer E_k has a uniform four-component structure: E_k = (Carrier_k, Predicate_k, Decoder_k, Invariant_k). The template is preserved under enrichment: each layer’s invariant flows into the next layer’s carrier.

Layer Template

Summary

Each enrichment layer E_k has a uniform four-component structure: E_k = (Carrier_k, Predicate_k, Decoder_k, Invariant_k). The template is preserved under enrichment: each layer’s invariant flows into the next layer’s carrier.

Statement

%
\label{def:layer-template}
An \textbf{enrichment layer} $\Elayer{k}$ is a quadruple
\begin{equation}\label{eq:ch05-layer-template}
    \Elayer{k} \;=\;
    \bigl(\,
        \mathrm{Carrier}_k,\;
        \mathrm{Predicate}_k,\;
        \mathrm{Decoder}_k,\;
        \mathrm{Invariant}_k
    \,\bigr),
\end{equation}
where:
\begin{enumerate}
    \item $\mathrm{Carrier}_k$ is the class of objects
          at enrichment depth~$k$---the \emph{raw material}.
    \item $\mathrm{Predicate}_k$ is the admissibility condition
          selecting well-formed objects---the \emph{gate}.
    \item $\mathrm{Decoder}_k$ is the canonical map
          extracting invariant information---the \emph{instrument}.
    \item $\mathrm{Invariant}_k$ is the stable datum
          the decoder produces---the \emph{output}
          that survives passage to the next layer.
\end{enumerate}
The four components are inherited from the ABCD chart:
$A \mapsto \mathrm{Carrier}$,
$B \mapsto \mathrm{Predicate}$,
$C \mapsto \mathrm{Decoder}$,
$D \mapsto \mathrm{Invariant}$.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-03.jsonl line 10
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part01/ch05-the-layer-template.tex lines 68-98

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Enrichment.LayerTemplate
• Name: LayerTemplate

Dependencies

• Canonical: III.D04

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.