DEF0260canonicalv1Gap Constant Γ*
Γ* = inf{Δ(f,n) : f non-trivial, n ≥ n₀}. The gap constant is computable at each finite primorial level and stabilizes as depth increases.
Payload
Gap Constant Γ*
Γ* = inf{Δ(f,n) : f non-trivial, n ≥ n₀}. The gap constant is computable at each finite primorial level and stabilizes as depth increases.
Gap Constant Γ*
Summary
Γ* = inf{Δ(f,n) : f non-trivial, n ≥ n₀}. The gap constant is computable at each finite primorial level and stabilizes as depth increases.
Statement
\label{def:gap-constant}
Let $\{V_n\}$ be an NF-discrete tower with contractive defect functional. The \emph{gap constant} is
\begin{equation}
\Gamma^* \;=\; \inf\bigl\{\, \Delta(f, n) \;\bigm|\; f \in V_n \text{ non-trivial},\; n \geq n_0 \,\bigr\},
\label{eq:ch39-gap-constant}
\end{equation}
where $n_0$ is the smallest primorial depth at which both (H1) and (H2) hold, and ``non-trivial'' means $f$ is not NF-stabilized (i.e., $\Delta(f,n) > 0$).
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 105 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch39-the-tau-gap-meta-theorem.texlines 57-66
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Physics.GapTheorem - Name:
gap_constant_check
Dependencies
- Canonical: III.T26
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.D45gap-constantdef:gap-constantRelease 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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