Chapter 35: The Strong Sector and NF Discreteness

This chapter opens the Yang–Mills block (Chapters 38–40) by isolating the strong sector—the C-sector from the 4+1 decomposition (the relevant definition, Ch. 10), instantiated at enrichment level E₁. The strong sector is governed by the generator η and carries the χ_–dominant spectral content that will underpin the mass-gap argument. We prove the NF Discreteness Lemma: the normal-form tower ℤ/Prim(k)ℤ admits at most Prim(k) distinct configurations in the C-sector at each depth k, a granularity that is not imposed but earned from K3 divisibility. We then define τ-admissible gauge data—the Yang–Mills analog of τ-admissible fluid data (the relevant definition, Ch. 34)—and preview how discreteness forbids the gap from closing.