First-Principles Derivation of the Bethe-Weizsäcker Semi-Empirical Mass Formula from the Fundamental Speed Theory

We present a first-principles derivation of the Bethe-Weizsäcker semi-empirical mass formula—one of the oldest and most successful models in nuclear physics—from the Fundamental Speed Theory (FST). Each term of the formula is shown to emerge from the FST effective gravitational coupling G_{\text{eff}}, which is governed by the motion principle G_{\text{eff}} \propto \rho M v / R. The volume term arises from the saturated effective coupling G_{\text{eff}}^{\text{sat}}(A) \propto A^{-1/3}, explaining the near-constancy of nuclear binding energy per nucleon. The surface term emerges from the gradient of G_{\text{eff}} across the nuclear surface. The Coulomb coefficient is derived exactly as a_c = 0.691 MeV, in 97% agreement with the experimental value. The asymmetry term is obtained from the isospin-dependent modification of G_{\text{eff}} in asymmetric nuclear matter, combined with the Fermi energy contribution, yielding a_a \approx 23.7 MeV in excellent agreement with experiment. The pairing term is acknowledged to require the quantum extension of FST. The derivation reduces the number of free parameters in the Bethe-Weizsäcker formula from five to three, while providing the physical origin and scaling behavior of each term from a unified theoretical framework. Complete dimensional analysis and detailed derivations are provided in the appendices