R-layer Mode Theory VIII: Effective Field Construction of Wall-Localized Modes

R-layer Mode Theory VIII develops the effective field theory governing the internal modes localized on domain walls within the R-layer framework. Building on the bound-state structure of Volume VI and the matter–gauge correspondence of Volume VII, this volume derives the complete 4D effective action for wall-localized modes, including kinetic terms, mass terms, mixing, gauge interactions, and Yukawa couplings. The geometric origin of gauge symmetry is formulated through the connectivity of the wall network, and hierarchical Yukawa structures naturally emerge from spatial localization of internal modes. The running of effective parameters is interpreted as a geometric effect of the wall configuration. This Version 2 update adds the section “Declaration of Generative AI and AI-assisted Technologies in the Writing Process” and includes minor textual corrections.