Neutrino masses and the Hubble constant as two measurements of one meV quantum: predictions for JUNO

If one mass quantum sets both the neutrino masses and the dark-energy scale, neutrino oscillation data measure the Hubble constant. The quantum is the geometric mean of the Planck and Hubble masses, k = p ℏmP H0/c2 ≈ 4.2 meV, the scale that saturates the Cohen– Kaplan–Nelson bound. With the spectrum mi = k(ni + 1/4π) and winding numbers (0, 2, 12), the two splittings measured by JUNO each give the Hubble constant, H0 = 65.7 ± 0.7 and 66.0 ± 0.7 km s−1Mpc−1 , in agreement with each other, and the ratio of the splittings, 33.79 with no free parameter, agrees with JUNO’s 33.96 ± 0.50. The offset 1/4π is the solid-angle average of one null direction at the mass point, the geometric form of a spin- 1 2 state. The spectrum predicts H0 = 65.9 ± 0.5 km s−1Mpc−1 from oscillation data alone, normal ordering, m1 = 0.33 meV, Σmν = 59.3 meV and Dirac neutrinos, and we register the measurements that would exclude it. The offset was identified after JUNO’s first measurement of both splittings, so the present agreement is not evidence; and the predicted H0 lies 2.2σ below the value Planck infers within ΛCDM and 6.2σ below the local distance-ladder value, so the spectrum requires the Hubble tension to be resolved on the side of the low value.