The Stabilization Spectrum: A Methodological Framework and Interpretive Escalation Protocol for Structural Regimes

The Stabilization Spectrum is proposed as a theoretical-methodological framework for describing and comparing structural regimes. This approach is applied when local parameter tuning or standard accounting for systematic errors fails to reconcile data from operationally distinct observation channels. The core principle is procedural: a stronger regime-level interpretation does not automatically follow from the mere fact of an anomaly. Interpretive escalation requires the execution of a rigorous baseline protocol comprising six mandatory elements: (1) definition of channels, (2) a candidate invariant, (3) a class of admissible transformations, (4) a transition rule, (5) a negative test with a failure criterion, and (6) a fallback explanation. This work does not establish a new empirical model, physical theory, or machine learning architecture. Its contribution lies in providing a unified vocabulary for the interdisciplinary comparison of effective descriptions. Technical tools - including topological data analysis (TDA), computation of η-proxies, bootstrapping, adversarial testing, or certification procedures - are treated strictly as optional computational implementations rather than universal requirements of the approach. Operational applicability is demonstrated on cosmological tensions (H0, S8, large-angle CMB anomalies) and the phenomenon of sudden generalization (grokking). These phenomena serve not as automatic proofs of new physics or cognitive mechanisms, but as testing grounds. They illustrate how candidate regime interpretations are retained only after successfully passing pre-defined validation procedures.