From Evidence to Evident: Decisive Cosmological Evidence for the Normal Neutrino Mass Hierarchy

Cosmological data have reached the precision needed to turn the neutrino mass ordering from a weak Bayesian preference into a decisive model-selection test. We compute the evidence for the Normal and Inverted Hierarchies by combining DESI DR2 clustering with NuFIT oscillation data. In baseline CDM, DESI DR2 plus Planck CamSpec gives m nu<0.0642, eV at 95% confidence, close to the normal-ordering floor, m nu NH 0.059, eV, but well below the inverted-ordering minimum, m nu IH 0.099, eV. Thus the inverted hierarchy lies in the tail of the cosmological likelihood. The Bayes factor K=P(D NH)/P(D IH) exceeds 460 even for a conservative reference prior, and remains strong, K>40, in baseline-model extensions. We show that this result is robust to the choice between a reference prior and a physically motivated logarithmic hierarchical prior, marking the transition from prior-sensitive evidence to likelihood-dominated exclusion of the inverted hierarchy within standard cosmology. Embedding these priors in the two-dimensional design space of measure (logarithmic versus linear in mass) and structure (hierarchical versus non-hierarchical), we find that all four prior constructions give decisive evidence under DESI DR2, with residual prior dependence governed mainly by the measure -- a factor about!10 in K -- rather than by the hierarchy assumption. At the prior-family level, the evidence favors the SJPV prior predictive over HS by a Bayes factor above 4,700 across each matched-support variation tested. The favored normal ordering pushes the effective Majorana mass to the few-meV regime, with median m beta beta=3.28, meV and 95% credible interval 0.95<m beta beta<11.55, meV, below the inverted-ordering target for upcoming neutrinoless double-beta decay experiments.