Physical Realizability Predicate

Formal predicate Phys(M) characterizing physically realizable TMs. Satisfies all three conditions of a host-level property (III.D70): it quantifies over all possible physical instantiations, requires E₃ vantage, and is not capturable at E₂. ZFC cannot internalize this predicate.

Physical Realizability Predicate

Summary

Formal predicate Phys(M) characterizing physically realizable TMs. Satisfies all three conditions of a host-level property (III.D70): it quantifies over all possible physical instantiations, requires E₃ vantage, and is not capturable at E₂. ZFC cannot internalize this predicate.

Statement

\label{def:physical-realizability-predicate}
A Turing machine~$M$ is \textbf{physically realisable} if there exists
an $\Elayer{1}$-object~$O$ in Category~$\T$ such that
$O$~hosts $M$'s operational closure---the
Code--Execution--Code cycle of~$M$ as a physical process
(Definition~\ref{def:physical-e2-agent}).
Formally:
\[
  \mathrm{Phys}(M)
  \;\;\stackrel{\mathrm{def}}{=}\;\;
  \exists\, O \in \operatorname{Obj}(\Elayer{1})
  \;:\;
  O \;\text{hosts}\; M.
\]

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-03.jsonl line 206
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part09/ch80-the-zfc-provability-horizon.tex lines 107-123

Lean / Formalization Notes

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

Dependencies

• Canonical: III.D77, III.D70

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.