By linking the string theory vacuum landscape to axion mass via zeta-function regularization, we derive an energy value equal to the product of the Rydberg energy unit, the fine structure constant, and the electron-proton mass ratio (hcR∞αµ-1). The resulting value of 54 μeV is consistent with the 45-65 μeV range predicted by cosmological lattice simulations. The QCD axion is identified as a dark matter candidate, with its mass presented as a mathematically necessary feature of the universe's vacuum field geometry. Beyond numerical coincidence, these results imply a fundamental connection between particle mass emergence and vacuum geometry, while providing indirect support for the axion as a viable candidate for both the strong CP problem and cold dark matter.