Dark Matter as Energy-Depleted Vacuum State: Galactic Rotation Curves and the Radial Acceleration Relation from Hyper-Elastic Continuum Mechanics

We propose that the observational signatures attributed to dark matter arise from region sof the vacuum substrate with reduced mode occupancy and energy-depleted vacuum states—rather than from a distinct particle species. Within the Triple-Point Vacuum (TPV) hyper-elastic continuum framework, such depletion stiffens the effective shear modulus, modifying the local refractive index and producing gravitational lensing and rotational support without stable quanta, electromagnetic coupling, or new degrees of freedom. We derive a TPV interpolation function for centripetal acceleration from the quadratic elastic energy of the substrate and test it against the full Spitzer Photometry and Accurate Rotation Curves (SPARC) dataset of 175 disk galaxies (3,391 data points). The Radial Acceleration Relation is reproduced with a single fixed scale a0 = 1.2 × 10−10 m s−2 and no per-galaxy free parameters; this scale is derived from vacuum lattice relaxation rather than fitted, representing a parameter-free prediction of the framework. The vacuum depletion field gic(r) = gobs − gbar is physically structured across morphologically diverse galaxies. The TPV prediction achieves RMS scatter of 0.332 dex across the full sample. By eliminating particulate substructure, this continuous framework natively avoids the cusp–core and missing satellites problems, and provides a qualitative constitutive mechanism for addressing cluster-scale lensing offsets (e.g., the Bullet Cluster) without dark substructure or baryonic feedback tuning.