The proton as a closed vortex ring in a superfluid vacuum: a zero-parameter formula for its mass, radius, and G, with pre-registered falsification conditions

We report a closed relation, containing no adjustable parameters, that connects the proton mass, the proton charge radius, the fine-structure constant α, and Newton's constant G, obtained by modelling the proton as a quantized vortex ring in a superfluid vacuum. All mathematics employed is standard: the Gross-Pitaevskii equation for the vortex core, and classical thin-ring energetics (Lamb; Saffman; Roberts-Grant). The relation makes three statements testable by experiments now running or imminent: (i) r_ch = 4ℏ/(m_p c) = 0.841236 fm, consistent within 1σ with all post-2010 determinations and decidable by the MUSE muon-proton scattering experiment; (ii) m_p = 938.263 MeV from the formula against the measured 938.272 MeV, a 9 ppm agreement lying inside the propagated uncertainty of G; and (iii) inverted, G = 6.674172(32) × 10⁻¹¹ m³ kg⁻¹ s⁻², within 1σ of CODATA-2022 and 0.2σ of the HUST time-of-swing measurement, taking a falsifiable side in the long-standing dispersion among laboratory G determinations. We present the mass relation in the spirit of Balmer's 1885 formula: an exact-looking, parameter-free empirical regularity whose full derivation is open at identified steps, each stated precisely. All assembly freedoms are audited by exhaustion, and falsification conditions are stated in advance of the deciding measurements.