Physical Admissibility Theorem

Every physically realizable Turing machine is τ-admissible. E₁ constraints (finite spatial extent, causal locality, bounded energy) block all Five Forbidden Moves. Combined with the Move-Bridge Correspondence (III.T43).

Physical Admissibility Theorem

Summary

Every physically realizable Turing machine is τ-admissible. E₁ constraints (finite spatial extent, causal locality, bounded energy) block all Five Forbidden Moves. Combined with the Move-Bridge Correspondence (III.T43).

Statement

\label{thm:physical-admissibility}
Let $M$ be a physical $\Elayer{2}$ agent
(Definition~\ref{def:physical-e2-agent}).
Then $M$ is $\tau$-admissible
(Definition~\ref{def:tau-admissibility}):
\[
M \;\text{physically realizable}
\quad\Longrightarrow\quad
M \in \operatorname{Adm}_{\tau}(k_0)
\;\;\text{for some}\;\; k_0 < \infty.
\]

Proof / Justification

By the Move-Bridge Correspondence
(Theorem~\ref{thm:move-bridge-correspondence}, Ch.~65),
$\tau$-admissibility fails if and only if the computation
invokes at least one forbidden move.
Section~\ref{sec:ch78-five-forbidden-physical} showed a physical
$\Elayer{2}$ agent cannot perform any of M1--M5.
Hence $M$ is $\tau$-admissible.
The width $k_0$ is bounded by the carrier's primorial depth.

Source Context

• Registry source: book-03.jsonl line 200
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part09/ch78-physical-turing-machines.tex lines 197-210

Lean / Formalization Notes

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

Dependencies

• Canonical: III.D77, III.D69, III.T43

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.