Toward a Renormalization Group Foundation for q-Deformed Galactic Dynamics: Three Conjectures

The q-deformed Effective Field Theory (q-EFT) framework has demonstrated competitive empirical performance against both NFW dark matter and MOND across 175 SPARC galaxies {Ref1}, but its microscopic theoretical foundation remains incomplete. In particular, the mechanism by which Planck-scale quantum deformation propagates to galactic-scale dynamics across thirty orders of magnitude has not been established. We propose three conjectures that together outline a path toward a rigorous microscopic foundation. Conjecture~1 identifies the topological phase-locking mechanism of q-EFT with the universality class of the Berezinskii--Kosterlitz--Thouless (BKT) transition, providing a natural explanation for the empirical morphological boundary of model applicability. Conjecture~2 proposes that the MOND acceleration scale a₀ corresponds to a stable infrared fixed point of the renormalization group flow of the q-deformation parameter, removing its status as an unexplained empirical constant. Conjecture~3 proposes that q-deformation induces effective non-commutativity of spacetime coordinates in the strong-field regime, providing a natural ultraviolet cutoff that recovers standard GR near compact objects. These conjectures are presented as a research agenda, not as established results; their verification requires substantial further mathematical development.