Matter-Originated Spacetime Gradient Model (MOSGM): A Phenomenological Gravity Model with Galaxy-Scale Constraints from the SPARC Sample

We present the Matter-Originated Spacetime Gradient Model (MOSGM), a phenomenological modification to baryonic gravitational acceleration motivated by spacetime gradient considerations. The model introduces a bounded interpolating function of the form g_obs = g_bar [1 + κ(μ(x) − 1)], where x = √(g_bar/a0), μ(x) = 1/(1 − e^(−x)), and κ = (e − 1)⁻¹. We evaluate MOSGM using the SPARC dataset of 171 late-type galaxies and compare its performance with the standard MOND algebraic interpolating function under a consistent analysis pipeline. Each model is assessed at its respective optimal stellar mass-to-light ratio: Υ_disk = 0.85 for MOSGM and Υ_disk = 0.50 for MOND. MOSGM achieves a median Pearson correlation of 0.959 between observed and predicted rotation velocities, compared to 0.958 for MOND. The median RMS residual is 14.63 km/s for MOSGM versus 13.98 km/s for MOND. MOSGM exhibits a near-zero median bias of +0.20 km/s, compared to +4.20 km/s for MOND. These results demonstrate that MOSGM reproduces galaxy rotation curves with accuracy comparable to MOND while exhibiting reduced systematic bias. We do not claim that MOSGM supersedes MOND; rather, it provides a competitive alternative framework for galactic dynamics whose phenomenological performance motivates further theoretical development.Notes-This work presents a phenomenological gravity model evaluated on observational data. Theoretical derivation of the interpolating function remains an open area for future work.