A Diagnostic for Rapid Identification and Navigation of Large Observable Spaces

This paper introduces a scale-mixing diagnostic framework designed to accelerate the identification, classification, and navigation of large observable spaces. Rather than proposing new physical dynamics, the framework operates as a pre-analysis tool that distinguishes kernel-protected observables from mixing-induced, projection-dependent quantities using operator–spectral structure. Mixing is interpreted as operator-induced refraction, revealing effective geometry and contour structure without assuming a metric, coordinates, or detailed dynamical models. The framework shows how ratio-based observables can amplify refraction into illusory asymmetries, potentially leading to severe misinterpretation or global mislocation when integrated across scale. Importantly, the analysis does not assume smooth behavior: refraction may vary non-continuously across regimes, making local correction unreliable and motivating a global, mapping-based approach. Proof-of-concept applications demonstrate that the framework reliably classifies observables, detects regime boundaries, and reveals scale-dependent structure, while clarifying the limits of interpreting mixing as a universal rate proxy. Overall, the method provides a global navigation layer that complements existing local, model-specific techniques by rapidly orienting researchers within complex observable spaces and guiding where detailed analysis should be applied.