Yang-Mills Gap Theorem

Instantiate the τ-Gap Meta-Theorem for the strong (C) sector: Γ*_s > 0. The τ-internal mass gap is a structural consequence of NF discreteness. Does NOT solve Clay YM (requires identifying τ strong sector with SU(3) gauge theory).

Yang-Mills Gap Theorem

Summary

Instantiate the τ-Gap Meta-Theorem for the strong (C) sector: Γ*_s > 0. The τ-internal mass gap is a structural consequence of NF discreteness. Does NOT solve Clay YM (requires identifying τ strong sector with SU(3) gauge theory).

Statement

\label{thm:yang-mills-gap-theorem}
Let $\{\operatorname{Strong}_{E_1}^{(k)}\}_{k \geq 1}$ be the NF-discrete tower of C-sector gauge configurations, equipped with the strong defect functional $\Delta_C$ (Definition~\ref{def:strong-defect-functional}). Then the strong-sector gap constant
\begin{equation}
\Gamma^*_s \;=\; \inf\bigl\{\, \Delta_C(\mathfrak{g}_k, n) \;\bigm|\; \mathfrak{g}_k \text{ non-trivial},\; n \geq n_0 \,\bigr\}
\label{eq:ch40-strong-gap-constant}
\end{equation}
satisfies $\Gamma^*_s > 0$. Every non-trivial $\tau$-admissible gauge configuration carries a strictly positive defect, uniformly bounded below across all primorial depths.

Proof / Justification

No immediate manuscript proof block was extracted in this pilot run.

Source Context

• Registry source: book-03.jsonl line 107
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch40-the-yang-mills-mass-gap.tex lines 101-110

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Physics.GapTheorem
• Name: yang_mills_gap_check

Dependencies

• Canonical: III.T26, III.D43, III.D44

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.