Structural Integrity Invariant and Its Domain of Definition

Version 5 of the Structural Integrity Invariant framework. This version formalizes the domain of definition of the invariant in arbitrary n dimensions and clarifies its behavior across finite, infinite, and limiting regimes. The formulation consolidates previous developments, including explicit 4D and 12D cases, into a unified and closed theoretical structure. The work is presented as a non-commercial theoretical preprint and supersedes all previous versions. This deposit contains a reference implementation of the Root-10 structural validation protocol. The material is archived for documentation and timestamping purposes. Access to the source files is restricted. This advanced edition formalizes the volumetric doubling of the cube as a structural invariant, achieved through a fixed irrational scaling factor rather than linear expansion. The result demonstrates a closed geometric system where stability emerges from proportional necessity, not approximation.