We explore a first-principles geometric framework to evaluate the precise frequency corrections in the atomic hydrogen 1S→2S transition by analyzing the coordinate strain of a bounded quantum vacuum. By extending the Einstein Equivalence Principle (EEP) to localized quantum states, we model the electron wavepacket as an extended matter wave whose internal phase clock modulates under intense non-inertial proper acceleration. Demanding that the contracting local Rindler horizon is bounded by the particle's irreducible Compton wavelength yields a maximum proper acceleration ceiling u2044 . Applying this constraint to the hydrogen ground state yields a metric modulation parameter . This coordinate-layer regularization introduces a geometric potential shift of 243.74 Hz, offering a novel, non-perturbative perspective that aligns closely with the high-precision spectroscopy data (2,466,061,413,187,018±11 Hz) tracked by the Max Planck Institute of Quantum Optics.