THM0161canonicalv1τ-Gap Meta-Theorem
Any NF-discrete tower with contractive defect functional and bounded sector extraction has a spectral gap. Γ* = inf{Δ(f,n) : f non-trivial, n ≥ n₀} > 0. Proof entirely τ-internal: no QFT, no gauge groups, no Lagrangians.
Payload
τ-Gap Meta-Theorem
Any NF-discrete tower with contractive defect functional and bounded sector extraction has a spectral gap. Γ* = inf{Δ(f,n) : f non-trivial, n ≥ n₀} > 0. Proof entirely τ-internal: no QFT, no gauge groups, no Lagrangians.
τ-Gap Meta-Theorem
Summary
Any NF-discrete tower with contractive defect functional and bounded sector extraction has a spectral gap. Γ* = inf{Δ(f,n) : f non-trivial, n ≥ n₀} > 0. Proof entirely τ-internal: no QFT, no gauge groups, no Lagrangians.
Statement
\label{thm:tau-gap-meta-theorem}
Let $\{V_n, \pi_{n+1,n}\}$ be a tower satisfying hypotheses \emph{(H1)} and \emph{(H2)} above. Then the gap constant satisfies $\Gamma^* > 0$.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 104 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch39-the-tau-gap-meta-theorem.texlines 79-83
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Physics.GapTheorem - Name:
tau_gap_meta_check
Dependencies
- Canonical: III.T09, III.D23, III.T15, III.T14, III.P16, III.D44
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.T26gap-meta-theoremthm:tau-gap-meta-theoremRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (2)
Appears in (1)
Downstream uses (computed) (4)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.