This paper examines a purely geometric model describing the continuously differentiable transition between a transcendental damping function and a harmonic phase oscillation at a vacuum interface. Assuming a resonant tunneling probability of exactly 1, this resulting system of transcendental equations yields a dimensionless base coupling value of... By extending the model to include an alternating perturbation series simulating the higher modes of vacuum fluctuations, and introducing a self-consistent topological projection factor—which describes the transition from the transverse degrees of freedom of the two-dimensional interface to the full three-dimensional exit geometry—the system converges to a purely theoretically derived limit of: αModel = 0.007297352563398466091220709349 Initial analyses—utilizing a theory proposed by the author that yields a universal field equation for quantum gravity—strongly suggest that both the alternating perturbation series and the geometric dimensional ratio are direct effects arising from vacuum fluctuations. The convergence value calculated here shows remarkable numerical agreement with the experimental CODATA value of the fine-structure constant, accurate to the eleventh decimal place.Furthermore, the model's fundamental consistency is not limited to the astrophysical low-energy scale: under scale transformations, the system's inherent dynamics reproduce the renormalization-group "running" of a universal coupling constant, as described in quantum field theory. At the electroweak scale, the model converges precisely to the value . This exact reproduction of the Z-boson mass demonstrates that the geometric principle presented here mathematically fully determines physical reality across a wide range of energy scales.