Scale-Invariant Boundary–Residue Translation: A Structural Operator for Cross-Scale Observability Demonstrated via Black Hole Radiation

This work introduces a scale-invariant structural operator describing how physical systems become observable through boundary-mediated residue emission. The framework formalizes the translation from internal state to measurable datum via interface constraints and is demonstrated using black hole radiation as the dominant case study. A cosmological comparison using cosmic microwave background radiation is provided as a global reference example. Expressed in normalized form, the operator reveals structural alignment across systems of vastly different scale and composition. The framework does not propose new physical laws but instead provides a diagnostic comparison method for identifying shared governing constraints across domains. Applicability conditions and falsifiability criteria are specified.