Chapter 31: The τ-Gap Meta-Theorem

The τ-gap meta-theorem states: any NF-discrete tower on τ³ with contractive defect functional and bounded sector extraction has a positive spectral gap Γ^* = ∈f{Δ(f,n)} > 0. This is a structural theorem about the spectral geometry of τ³, not a conjecture about a specific theory. It applies to any sector satisfying its hypotheses. The C-sector (strong force) is one such instance, and the Yang–Mills mass gap—a Clay Millennium Prize Problem—follows as a corollary.