Structural Spectral Diagnostics of Scalability in Quantum Architectures: Layer I

Scalability remains a central challenge in large-scale quantum architectures. While device-level characterization is essential, many scalability constraints originate at the architectural level, where global coordination limits and asymptotic instabilities emerge prior to layout, compilation, or hardware modeling. We introduce a structural admissibility framework positioned as a pre-hardware diagnostic layer for architecture-level scalability assessment. Architectures are modeled as controlled scaling families, and admissibility is determined by a set of structural functionals governing growth consistency, compositional refinement, and perturbative stability. These functionalsestablish whether a family supports coherent large-scale expansion before physical realization. To obtain measurable diagnostics, each structural instance is associated with a symmetric operator from a minimally specified axiomatic class. The smallest non-zero eigenvalue defines a spectral gap observable whose scaling yields a coherence-like indicator, an effective structural dimension estimate, and a quantitative measure of scaling fragility. Baseline experiments using the normalized graph Laplacian show that purely structural observables already separate distinct scaling regimes—such as mediation-dominated 1D chains and dimension-supported 2D grids—without invoking device-level noise models.