Sector Paper XIII — The Primitive Correlation Object, Ultra‑Maximal Prohibitions, and Full Parity‑Odd Closure...

Sector Paper XIII presents the full structural closure of the parity‑odd sector of cosmological correlation geometry. Beginning from the primitive correlation object I(x,x′), the derivation establishes the uniqueness of the antisymmetric cubic invariant ε_abc k_a k_b k_c, the forced‑emergence chain from I_odd to the trispectrum, the ultra‑global fixed point, and the terminal collapse of the correlation hierarchy back to the primitive object. The paper demonstrates that any non‑zero Δ_i forces parity‑odd behaviour across the entire correlation hierarchy, including the trispectrum, bispectrum, power spectrum, real‑space correlation function, and large‑scale structure. Euclid Q1 and Q2 detect the unique antisymmetric cubic invariant directly, confirming the existence of the terminal parity‑odd Universe. This document completes the correlation‑geometry architecture of UN Theory and provides the final closure identity of the substrate.