A Space-Matter Continuum: Resolving Galactic Anomalies without Dark Matter

The dark matter (DM) paradigm successfully describes large-scale structure and cosmic microwavebackground anisotropies, yet faces persistent challenges at galactic scales. The diversity of galacticrotation curves, the missing satellites problem, and anomalous substructure in gravitational lensessuggest either complex baryonic physics or modifications to the DM model. We propose a unifiedspace-matter continuum (SMC) where both gravity and matter emerge as phases of a fundamentalscalar field ϕ. The theory naturally explains: (i) the radial acceleration relation of spiral galaxies,(ii) the bimodal distribution of the acceleration scale λ, and (iii) anomalous lensing substructureas self-gravitating ϕ-solitons. We analyze the SPARC galaxy sample and lens system B1938+666,finding excellent agreement with SMC predictions. The theory makes testable predictions for VLBIobservations of lensed quasars and provides a geometric alternative to particle dark matter. Detailedderivations show that the effective gravitational coupling Geff emerges naturally from condensationenergy density ρcond, with geometric consistency requiring β = 1/(8π). 10.5281/zenodo.18269890