Regulated Operators under Constrained Accumulation

This paper examines whether regulated accumulation alone is sufficient to force essential self-adjointness and compact resolvent for operators defined on admissible domains. [1][2][3][4] No compact embedding theorems are assumed. No spectral conjectures are invoked. The author explicitly pressure-test’s domain closure, deficiency indices, and resolvent compactness under iterative accumulation control. Using discretized operator models, thus comparing regulated and unregulated growth regimes and demonstrates that spectral discreteness arises from saturation rather than imposed topology. The results remain falsifiable at each structural stage.