PRP0084canonicalv1Gap Stabilization
The gap constant Γ* converges (stabilizes) as primorial depth increases, by tower coherence. Computable at each finite level.
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Gap Stabilization
The gap constant Γ* converges (stabilizes) as primorial depth increases, by tower coherence. Computable at each finite level.
Gap Stabilization
Summary
The gap constant Γ* converges (stabilizes) as primorial depth increases, by tower coherence. Computable at each finite level.
Statement
\label{prop:gap-stabilization}
The sequence $\{\Gamma_n\}_{n \geq 1}$ is non-decreasing and converges:
\begin{equation}
\Gamma_1 \;\leq\; \Gamma_2 \;\leq\; \Gamma_3 \;\leq\; \cdots
\qquad\text{and}\qquad
\Gamma^* \;=\; \lim_{n \to \infty} \Gamma_n \;=\; \inf_n \Gamma_n \;\geq\; \Gamma_1 \;>\; 0.
\label{eq:ch39-gap-stabilization}
\end{equation}
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 106 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch39-the-tau-gap-meta-theorem.texlines 165-175
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Physics.GapTheorem - Name:
mass_existence_check
Dependencies
- Canonical: III.D45, III.T09
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.P17gap-stabilizationprop:gap-stabilizationRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
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.