From Galactic Dynamics to Effective Force Laws in Fundamental Speed Theory (FST): Dominant-Degree Selection, Matching, and Testable Predictions

We develop an effective classical framework derived from Fundamental Speed Theory (FST) in which familiar force laws arise as distinct dominant odd-degree sectors of a single nonlinear field expansion. Working in the static weak-field limit, we define a dimensionless temporal perturbation and use the spacetime-fabric relation to connect field gradients to the Newtonian potential. We introduce a dominant-scale analysis that selects, at each length scale, the energetically preferred effective degree n = 2k + 1, providing a classical mechanism that organizes the behavior from galactic to subnuclear distances. Within this effective description, long- and short-range regimes are characterized by Laplace/Poisson or Helmholtz-type equations, yielding Newtonian, Coulomb, Yukawa-like, and confining behaviors in appropriate limits. The normalizations and screening scales of the electromagnetic, nuclear, and weak sectors are treated as matched effective parameters constrained by low-energy data (e.g., \alpha, m_{\pi}, M_{W}, M_{Z}, G_{F}, and hadronic scales), while the framework emphasizes the universal scaling structure and the selection mechanism for the dominant degree. We derive a set of testable predictions, including power-law force behaviors at short distances ( F \propto r^{- 1.1} for QCD, F \propto r^{- 1.09} for the weak force), the emergence of Maxwell's equations from the n = 5 sector, a relation between electromagnetic constants and Newton's constant G, and the absence of even-degree forces. We discuss limitations of the purely classical treatment and the requirements for a consistent quantum completion.