On the Mass of the Photon: Finite-Ray Inversion from Independent Mercury Excitation and Spectral Measurements

Mercury supplies two independent experimental coordinates for the photon: an electrical excitation energy and an optical wavelength. Harmonic Natural Physics (HNP) constructs a finite ray from the measured propagation support, obtains its mass, and resolves that mass into its photon population. For n = L/λ, elimination of the intermediate Harmonic action quantity gives M_ray = Eγ Δt_H²/L² and Mγ = Eγλ Δt_H²/L³. The mercury state yields Mγ = (2.4665 ± 0.0151) × 10⁻⁶¹ M, equivalent to (1.8478 ± 0.0113) × 10⁻⁵¹ kg. The photon Spin state gives p_Spin,γ = √(MγEγ) ∝ λ⁻¹/². Finite accumulation produces λ⁻³/² for a fixed-support ray and λ⁺¹/² for a fixed-power beam. The latter gives the square-root optical-torque null tested prospectively in the companion experiment. Exact SI values of h and c yield the corresponding exact photon-mass representation of the kilogram.