Neutrino mass hierarchy from a geometric progression and a spectral hypothesis for the hyperbolic 3-manifold m003

We propose a minimal hypothesis for the neutrino mass hierarchy: the three active neutrino masses follow a geometric progression m2 = km1, m3 = k^2m1. Using the experimentally measured mass splittings, updated with the first high-precision data from the JUNO experiment (∆m21)^2 = 7.50 × 10−5 eV^2), we obtain k = 5.6991. From this corrected geometric framework, we derive the absolute masses m1 = 0.001544 eV, m2 = 0.008797 eV, m3 = 0.050134 eV, and their sum mν = 0.0605 ± 0.002 eV. This sharp prediction sits just slightly above the physical lower limit of the normal hierarchy (∼ 0.0587 eV) and is testable by upcoming cosmological surveys (DESI, Euclid, Simons Observatory). We suggest that the factor k may have a spectral origin, namely the ratio of the first two eigenvalues of the Dirac operator on the Gieseking manifold m003 with a suitable spin structure. Notably, the Koide relation 2/3 appears as (3−1)/(4−1), possibly related to the Z/4 symmetry of m003.