Chapter 36: The τ

We prove the τ-Gap Meta-Theorem: any NF-discrete tower equipped with a contractive defect functional admits a strictly positive spectral gap. The argument is entirely τ-internal—no quantum field theory, no gauge groups, no Lagrangians. NF discreteness (Ch. 38) provides a minimal separation between distinct configurations at each primorial depth; defect contractivity (Ch. 35) prevents accumulation toward zero. These two properties together force the gap constant Γ^* to be strictly positive. We compute Γ^* explicitly at the first three primorial levels and prove that it stabilizes as primorial depth increases. The theorem is a meta-theorem because it applies to any sector satisfying the hypotheses—Yang–Mills (Ch. 40) is one instantiation, but the logic is not specific to gauge theory.