R-layer Mode Theory IX: Unified Theory of Gravity, Matter, and Gauge Structure

R-layer Mode Theory IX presents the unified theoretical framework in which gravity, matter, and gauge structure all emerge from a single underlying mode field. Building on the effective field theory of wall-localized modes developed in Volume VIII, this volume formulates the master action that unifies curvature response, bound-state matter fields, and gauge interactions generated by wall-network topology. The geometric origin of mass hierarchies, gauge symmetries, and cosmic structure is derived from the multi-scale organization of the R-layer. This Version 2 update adds the section “Declaration of Generative AI and AI-assisted Technologies in the Writing Process” and includes minor textual corrections, without altering the scientific content.