MUT n-Free Framework Application v7.11.1: NGC 3198 Rotation Curve Analysis

Section 7.11.1 explains why the Myo Min Aung Unified Theory n-free framework uses the spatial gradient of the resonance field Φ(r) rather than the field value itself when calculating galactic dynamics. The analysis shows that the additional gravitational acceleration arises from the derivative dΦ/dr, which is analogous to how forces emerge from potential gradients in classical physics. This formulation ensures dimensional consistency because the term (c²/2)(dΦ/dr) naturally produces acceleration units. Numerical testing with SPARC rotation curve data for NGC 3198 demonstrates that the gradient-based equation produces a smoother and physically consistent resonance field profile while achieving a better statistical fit than multiplicative formulations. The result confirms that the Φ(r) gradient acts as an effective enhancement to baryonic gravity, providing the additional acceleration required to maintain flat galaxy rotation curves without introducing dark matter halos.