The phenomenon of "dark matter," while a cornerstone of the standard cosmological model (ΛCDM), remains one of the most profound puzzles in modern physics due to the persistent null results in direct detection experiments. This paper presents an alternative paradigm where "dark matter" is not a new type of particle but rather an emergent gravitational effect arising from the dynamic response of the physical vacuum itself. We model the vacuum as a quantum substratum, described by a fundamental scalar field, Φ. We propose that this substratum is coupled to gravity, and its energy density is modified in the presence of baryonic matter. To test this hypothesis, we construct a mathematical model governed by a single, universal coupling constant, herein named the "Shota" constant (β_Sh), which dictates the strength of the interaction between the Φ-field and the gravitational potential of visible matter. The model is tested through numerical simulations on two astrophysically distinct galaxies: the dwarf, dark-matter-dominated UGC 128 and the massive spiral galaxy NGC 3198. The results demonstrate remarkable success. With a nearly identical value for the "Shota" constant, the model quantitatively reproduces the rotation curves of both galaxies. Crucially, it naturally explains the observed nonlinear relationship between baryonic mass and the "dark matter" effect, showing a much larger relative response in the low-acceleration regime of the dwarf galaxy. This provides a physical foundation for the empirical Baryonic Tully-Fisher Relation (BTFR). Our framework unifies the concepts of the "Quantum Substratum" and the "Gravitational Deficit Principle" into a single, predictive theory, offering a compelling new path toward resolving the dark matter puzzle without recourse to new particles.