<p class="MsoNormal" style="margin-bottom: 12.0pt; text-align: left; mso-line-height-alt: 12.0pt; layout-grid-mode: char; mso-layout-grid-align: none;" align="left">Quantum-Corrected Gravity from Non-Associative Gauge Theory Explains Galactic Rotation Curves Without Dark Matter

We propose a modified gravitational framework that introduces a Yukawa-type correction to Newtonian gravity, applied to a baryonic mass density described by a stretched-exponential profile. This formulation is theoretically motivated by algebraic spinor dynamics, which naturally generates a finite-range gravitational interaction. The resulting velocity profile incorporates both the standard gravitational potential and an exponential correction term, producing an analytic expression that we test against observational data. We apply this model to four astrophysical systems—two spiral galaxies (NGC 2403 and NGC 5055) and two galaxy clusters (Abell 2029 and Abell 2199)—which are known for exhibiting flat or rising rotation curves in their outer regions. For each system, we fit the model to observed orbital velocities and determine best-fit parameters characterizing the Yukawa strength and scale length. The fits show excellent agreement across all radii, particularly where Newtonian predictions typically underestimate velocities. Notably, this agreement is achieved without invoking non-baryonic dark matter or NFW-type halo profiles. These results suggest that a Yukawa-corrected baryonic model, grounded in spinor gravity, offers a viable explanation for the observed flattening of rotation curves in both galactic and cluster scales, and provides an alternative route to addressing the missing mass problem in astrophysics.