THM0168canonicalv1τ-Admissibility Collapse
τ-P_adm = τ-NP_adm. For every τ-admissible NP problem, CRT-structured witness search runs in polynomial time. Three-step proof: (i) constant-width Cook-Levin tableau, (ii) polynomial CRT refinement, (iii) Product-Meet Collapse.
Payload
τ-Admissibility Collapse
τ-P_adm = τ-NP_adm. For every τ-admissible NP problem, CRT-structured witness search runs in polynomial time. Three-step proof: (i) constant-width Cook-Levin tableau, (ii) polynomial CRT refinement, (iii) Product-Meet Collapse.
τ-Admissibility Collapse
Summary
τ-P_adm = τ-NP_adm. For every τ-admissible NP problem, CRT-structured witness search runs in polynomial time. Three-step proof: (i) constant-width Cook-Levin tableau, (ii) polynomial CRT refinement, (iii) Product-Meet Collapse.
Statement
\label{thm:tau-admissibility-collapse}
For every $\tau$-admissible NP problem,
\begin{equation}\label{eq:ch58-collapse}
\tau\text{-}P_{\mathrm{adm}}
\;=\;
\tau\text{-}NP_{\mathrm{adm}}.
\end{equation}
If $\Pi$ is an NP problem whose TTM verifier has finite interface
width $W(V) = k_0$, then witness search runs in time polynomial
in the primorial depth $k$.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 157 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part09/ch58-the-computational-bi-square.texlines 178-189
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Computation.CompBiSquare - Name:
tau_admissibility_collapse_check
Dependencies
- Canonical: III.D51, III.T31, III.D55, III.P22, III.P23, III.T32, III.D52
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
III.T33admissibility-collapsethm:tau-admissibility-collapseRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (1)
Appears in (1)
Downstream uses (computed) (2)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
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