Spectral Coherence Field Theory Constraint Structure and Operator Architecture of Coherent Physical Systems

We identify minimal structural requirements that any physical description must sat- isfy to represent persistent, coherent systems capable of internal dynamics. Rather than postulating new dynamical laws, we work at an architectural level, isolating constraints implied by the empirical fact that localized entities endure, remain measurable, and support stable internal motion. The first constraint is closure: coherence must be selec- tively retained rather than dispersed, which enforces an admissible boundary (physical or effective) and thereby supports resonance. In bounded or effectively bounded sectors, closure produces isolated spectral features—eigenmodes or long-lived quasi-modes—that render coherent configurations countable and stable. Spectral stability in turn requires self-adjoint operator structure so that observables remain real and evolution is norm- preserving. Finally, coherent internal motion requires a complementary skew-adjoint circulation/transport component, compatible with the stable spectral backbone but capable of generating nontrivial flow. These elements assemble into a unified operator architecture with three roles: admissibility (domain and boundary), closure/stability (self-adjoint spectral structure), and circulation/transport (skew-adjoint motion). The framework clarifies a common structural spine underlying quantum theory, field the- ory, and geometric constraint, while remaining agnostic about specific microscopic realizations.