Extended Structural Analysis of Local Infrared Rigidity

We present a structural stability analysis of the local infrared classification framework for Herglotz–Nevanlinna functions. Building upon the finite stratification theorem and the universality of the infrared exponent, we examine the robustness of the classification under pure point, continuous, and hybrid spectral configurations.We prove that, under the joint hypotheses of Herglotz structure, infrared locality, and algebraic dominant singularity, the infrared invariant reduces universally to the pair (Type, gamma), and no infinite strictly realizable hierarchy can arise within the local category.The analysis confirms that the algebraic continuous sector foliates rigidly by the exponent gamma, that the pure point sector collapses to a single meromorphic class, and that hybrid mixtures do not generate additional structural layers.This document provides an extended categorical consistency analysis supporting the finite infrared stratification principle.