Global Rigidity of Admissible Spectral Objects

This work examines abstract spectral data under a minimal set of global invariants: functional symmetry, multiplicative coherence, Riemann–von Mangoldt type asymptotics, and stability under admissible variations. No operator is constructed and no existence is assumed. The analysis is purely structural and eliminative. Under these invariants, the admissible class collapses to at most one equivalence class; any deviation violates admissibility and is excluded. The results establish conditional global rigidity of admissible spectral objects. Questions of realization, construction, or application lie entirely outside the scope of this work.