Universal Admissibility Theorem

ALL τ-native computation—at every enrichment level, whether physical (E₁-hosted) or abstract (E₃ diagrammatic)—is τ-admissible. The τ-Admissibility Collapse applies universally within Category τ: τ-P = τ-NP for all τ-native computation.

Universal Admissibility Theorem

Summary

ALL τ-native computation—at every enrichment level, whether physical (E₁-hosted) or abstract (E₃ diagrammatic)—is τ-admissible. The τ-Admissibility Collapse applies universally within Category τ: τ-P = τ-NP for all τ-native computation.

Statement

\label{thm:universal-admissibility}
Let $A$ be a $\tau$-native computational agent
at any enrichment level $\Elayer{n}$ ($n \in \{0,1,2,3\}$).
Then $A$ is $\tau$-admissible
(Definition~\ref{def:tau-admissibility}),
and the $\tau$-Admissibility Collapse applies:
\begin{equation}\label{eq:ch79-universal-collapse}
    \tau\text{-}P \;=\; \tau\text{-}NP
    \qquad \text{(universally within $\T$).}
\end{equation}
This holds for \textbf{all problems definable in~$\T$}.

Proof / Justification

No immediate manuscript proof block was extracted in this pilot run.

Source Context

• Registry source: book-03.jsonl line 204
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part09/ch79-abstract-computation-in-tau.tex lines 233-246

Lean / Formalization Notes

• Formalization: not_applicable
• Module: None
• Name: None

Dependencies

• Canonical: III.D78, III.D69, III.T43, III.T33

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.