Classical continuum theories such as the Navier–Stokes equations exhibit near-universal predictive success while admitting rare, highly localized breakdowns in the form of singular or near-singular behavior. These events are traditionally treated as mathematical pathologies and are often excluded from physical interpretation. This work reframes such breakdowns as structured transition signatures rather than failures. Using anomalous swirl patterns in fluid dynamics as a primary evidentiary domain, the paper extracts common features observed near unstable boundary regimes, including loss of local closure, persistence of global conservation laws, and the emergence of scale-invariant behavior. These features are shown to define a dimension-agnostic constraint that marks the limit of three-dimensional descriptive adequacy. Interpreted through the Dimensional Compatibility Unification (DCU) and Sandhi frameworks, the results suggest that apparent breakdowns signal transitions between descriptive regimes rather than inconsistencies in physical law. The paper emphasizes mapping such boundaries over proving global smoothness and highlights the role of AI-assisted searches in identifying rare instability configurations. A brief cross-domain correspondence with quantum tunneling is noted, positioning this work as a foundational step toward a broader, transition-centric understanding of physical models across domains.
Uthraa Murali (Sun,) studied this question.