A Structural-Regime Framework for Interdisciplinary Description: Interpreting Tensions in Cosmology and Machine Learning

Modern precision sciences, from cosmology to machine learning, increasingly encounter tensions in which accumulating data fail to consolidate a coherent picture and instead expose fractures between independent reconstruction channels. In such cases, a purely parametric description may be methodologically insufficient: a persistent tension can indicate not only measurement error or local systematics, but also reaching the limits of a given model class. This paper proposes a structural-regime framework: a categorically formalized methodological interface that provides a consistent vocabulary for configurations, morphisms, invariants, stabilizations, and phase-like transitions. The framework is designed to distinguish ordinary parameter mismatch from cases in which a tension may mark a boundary between effective regimes of description. Cosmological tensions, including H0 and S8, large-angle CMB anomalies, and the phenomenon of grokking in machine learning, are examined as pilot fields. Across these domains, the framework treats invariants operationally as reproducible cross-channel signatures and makes negative tests a constitutive requirement for any regime-level interpretation. The framework introduces a strict escalation criterion. It does not propose a new physical theory or AI architecture, nor does it replace standard Bayesian inference. Its value lies in narrowing the space of speculative interpretations by requiring algorithmically testable falsifiers before a tension is interpreted as a candidate indication of a phase-like or regime-level transition.