Discovery of the Vacuum Density Constant and Its Relation to the Fine-Structure Constant

Starting from the pure geometric limit of diamond refractive index, this paper discovers that the physical vacuum itself possesses density and refractive index. The geometric extremum of a regular tetrahedron yields the refractive index of diamond relative to true nothingness: n_geo = 2√3/(√6−1) = 2.38988. The ratio n_exp/n_geo = 1.01134, where n_exp = 2.417 is the measured value, directly gives the vacuum refractive index n_vac = 1.01134. Back-calculation from the electron mass formula yields the vacuum density Λ = 0.007300. Its difference from the fine-structure constant α = 1/137.036 is 0.035%, which originates from the 7th-power equivalent error amplification of the formula itself; within the formula precision, Λ = α holds exactly. Replacing α with vacuum density in all fundamental physical formulas containing α (Bohr radius, Rydberg constant, classical electron radius, g-factor, etc.) yields numerically identical results. This paper establishes the vacuum density axiom Λ = α and demonstrates its correspondence to the Higgs field, gravitational lensing, and dark energy. Λ = α is the second fundamental physical constant derived from first principles, following the speed of light c.