The Pandora Degeneracy: Non-thermal pressure, inference limits, and a joint diagnostic for galaxy dynamics.

Recent high-resolution simulations of dwarf galaxies have demonstrated that reproducing observed rotation curves and inner mass profiles requires substantial non-thermal dynamical support beyond collisionless gravity. Turbulence, feedback, magnetic fields, and cosmic-ray transport can all contribute to this support, often in partially degenerate ways. As a result, agreement between simulations and observations no longer uniquely identifies the physical mechanisms responsible, but instead admits families of explanations with similar macroscopic signatures. This paper formalises this situation as a problem of effective pressure degeneracy and examines the limits of inference imposed by commonly used diagnostics. We show that rotation-curve core shapes robustly diagnose the radial manifestation of additional support, but do not uniquely constrain its origin, while correlations with star-formation history or geometry and environment probe organising influences without encoding radial structure. To address this, we introduce a joint diagnostic framework in which these two observable classes define orthogonal axes of a diagnostic plane. Within this framework, the manifestation and organisation of dynamical support are separated, allowing competing explanatory classes to be distinguished without assuming a specific mechanism. The resulting mapping clarifies how simulations, phenomenological models, and observations jointly constrain the inference landscape, and identifies where degeneracy persists. Rather than proposing a new dynamical mechanism, this work provides a mechanism-agnostic, empirically grounded framework for organising existing evidence, guiding observational and simulation priorities, and sharpening inference in dwarf-galaxy dynamics