Chapter 32: Fluid Sectors and the Defect Functional

The 4+1 sector decomposition (the relevant definition, Ch. 10) was built for boundary characters on 𝕃. Here we apply the same template to τ-admissible fluid data (the relevant definition, Ch. 34), obtaining a sector-by-sector decomposition of the flow. Each sector inherits the split-complex structure e_+ / e_-, and the ω-coupling sector mediates inter-sector energy transfer. We then introduce the defect functional Δ, which measures how far fluid data deviates from canonical form at a given primorial depth, and prove that Δ is contractive under primorial refinement—the key estimate driving the Positive Regularity Theorem of Chapter 37.