A Phenomenological Unified Framework: Frequency-Dependent Yukawa Potentials Linking Gravity and Residual Nuclear Interactions via an Empirical Constant Relation

We present a phenomenological scalar field model that attempts to connect the long-range gravitational interaction and the short-range residual strong nuclear force through a generalized Yukawa-type equation with interaction-specific characteristic frequencies $\Omega$. For gravity, $\Omega = H_0$ yields effectively infinite range; for the residual nuclear force, $\Omega \approx m_p c^2 / \hbar$ yields $\sim$ fm range. The model is motivated by a striking empirical relation (accurate to 0.037\% using Planck 2018 $H_0$, and 0.584\% with 2025 combined CMB data) linking $G$, $H_0$, and atomic/quantum constants. We derive the force law, confront severe experimental constraints on massive gravity/Yukawa modifications, and discuss limitations in reconciling with general relativity and QCD.