Emergent Time Dynamics in Disk Galaxies: Explaining Flat Rotation Curves Without Dark Matter

Galactic rotation curves remain one of the central challenges in modern astrophysics. The standard ΛCDM framework explains the observed flatness of rotation curves through extended dark matter halos, while alternative approaches such as MOND invoke modifications of gravitational dynamics at low accelerations. This work investigates an alternative explanation based on the Discrete Expansion and Emergent Time (DEET) framework. In DEET, physical time is not assumed as a fundamental background parameter but emerges dynamically from the gradient flow of a scalar phase field Θ. Spatial variations in time production generate an effective acceleration that can influence galactic dynamics without introducing dark matter or modifying the baryonic mass distribution. A theoretical rotation-curve relation is derived and tested against a sample of 175 disk galaxies spanning a broad range of masses, morphologies, and baryonic fractions. The analysis focuses on the outer regions of galaxies where rotation curves are approximately flat and observational uncertainties are minimized. The results indicate that the DEET framework reproduces the observed outer-disk rotation behavior with high statistical accuracy across the majority of the sample. Deviations are primarily associated with galaxies exhibiting strong non-circular motions, bars, limited radial coverage, or other known observational complications. These findings suggest that flat rotation curves may be interpreted as manifestations of emergent time dynamics rather than evidence for dark matter halos. The work provides a falsifiable observational test of the DEET framework and establishes a direct connection between emergent time structure and galactic-scale dynamics.