Cross-Constrained Central-Engine Diagnostics in GRB–SN Systems

This work introduces Cross-Constrained Central-Engine Diagnostics (CCD), a methodological framework for evaluating gamma-ray burst (GRB) central-engine interpretations by combining two diagnostic layers that are often treated separately: engine-space plausibility and thermal--non-thermal temporal coherence. Engine-space diagnostics, such as the B_p--P_0 plane, test whether inferred central-engine parameters occupy physically meaningful regions of parameter space. Thermal--non-thermal coupling diagnostics test whether distinct emission components evolve as manifestations of a common engine-driven process. CCD proposes that a physically compelling interpretation should satisfy both conditions simultaneously. The framework is not a new emission model, progenitor class, or classification scheme. Rather, it is a consistency test designed to reduce interpretive ambiguity by asking whether inferred engine properties and multi-component emission behaviour remain mutually compatible within a single physical scenario. The paper develops the CCD framework, defines its diagnostic outcomes, identifies candidate applications in GRB--SN systems and anomalous or transitional GRBs, and formulates observationally testable predictions. These include correlated temporal transitions between thermal and non-thermal components, relationships between plateau energetics and thermal response, preferential occupation of viable engine-space regions by strongly coupled systems, and the emergence of diagnostically valuable outliers. CCD is particularly relevant for events that blur traditional GRB classification boundaries, including long-duration merger-like GRBs and progenitor-ambiguous transients. The framework provides a route toward increasing diagnostic specificity in the interpretation of GRBs and other engine-driven transients.