τ-Admissibility (E₂)

f is τ-admissible iff W(f) < ∞. τ-admissible computations need only finitely many primorial stages. The E₂ analog of the admissibility pattern from E₁ (NS fluid data, YM gauge data).

τ-Admissibility (E₂)

Summary

f is τ-admissible iff W(f) < ∞. τ-admissible computations need only finitely many primorial stages. The E₂ analog of the admissibility pattern from E₁ (NS fluid data, YM gauge data).

Statement

\label{def:tau-admissibility}
A TTM-computable function $f$ is \textbf{$\tau$-admissible} if its interface
width is finite:
\[
W(f) < \infty.
\]
Equivalently, there exists $k_0 \in \mathbb{N}$ such that for \emph{all}
input sizes $n$, the computation of $f$ on inputs of size $n$ stabilizes
at primorial depth $k_0$.
We say $f$ is \textbf{$\tau$-admissible at depth $k_0$} and write
$f \in \operatorname{Adm}_\tau(k_0)$.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-03.jsonl line 149
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part09/ch56-interface-width-and-tau-admissibility.tex lines 128-140

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Computation.Admissibility
• Name: tau_admissible_check

Dependencies

• Canonical: III.D53

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.