Universal Collapse II: Structural Regimes, Equivalence, and Structural Transitions

The Universal Collapse framework describes physical reality as an emergent structure arising from the dynamics of a scalar geometric field. In the preceding formulation, the field-geometric substrate provides a basis from which geometry, dynamics, matter, gravity, and observable structures may emerge as regime-dependent descriptions. The present work develops the next structural step of this framework: the mathematical characterization of regimes themselves. Rather than identifying a regime with a particular field configuration, we consider an admissible configuration space and introduce a structural representation, a structural equivalence relation, and the corresponding quotient space of regimes. Within this construction, a regime is represented as an equivalence class of structurally compatible configurations. A classification operator then associates admissible configurations with their corresponding structural regimes, allowing regime transitions to be described as changes of equivalence class. The construction also distinguishes structural transitions from dynamical attraction and from irreversible evolution. This distinction is important because a change of regime does not, by itself, imply the existence of an attractor or a fundamental arrow of time. Finally, the framework provides a formal bridge between regime transitions and the persistence of structural information, preparing the subsequent analysis of structural residues. The purpose of this work is therefore not to introduce a new scalar-field action, but to formalize and refine the structural organization of regimes within the Universal Collapse and Theory of Nothing framework.