TERM: Structural Closure via Discrete Spectrum, Invariant Fixation, and IR Spectral Rigidity

Building on the spectral architecture developed in the previous paper, we complete the structural layer of the framework by fixing both the spectral source and the renormalization invariant. First, we impose a minimal geometric constraint by defining the fourth‑order stability operator on a compact simplicial complex, yielding a discrete spectrum. Second, we introduce a global spectral action whose finiteness and extremality select a unique renormalization trajectory, thereby fixing the invariant I. These two ingredients eliminate the remaining structural freedom of the model. We further show that the infrared (IR) limit exhibits spectral rigidity: while absolute scales may evolve, the dimensionless spectral structure becomes asymptotically fixed. This leads to stable mass ratios and an effective second‑order dynamics at large scales. The resulting framework is structurally closed: operator, spectrum, invariant, and flow are mutually constrained and no longer independent inputs.