Second–Order Spectral Rigidity and the Yang–Mills Mass Gap

We show that spectral collapse in refinement limits is excluded under minimal rigidity assumptions.If admissible refinements are non-dense and first-order variations saturate, second-order coercivity follows and prevents accumulation at zero.All gapless limit scenarios are eliminated by compactness and spectral comparison.No construction or explicit spectral computation is required. Related work: Dirac-type operators and Weitzenböck identities illustrate second-order coercive mechanisms familiar in gauge theory; the present work does not rely on such structures, but abstracts the minimal spectral rigidity they reflect.