Geometry Selection of the Absolute Neutrino Mass Scal

The absolute neutrino mass scale is still unknown and is usually treated as a free parameter constrained only by external bounds. In this work we show that this view is incomplete. When the minimal seesaw is treated as an inverse problem in observable space, the mapping from high-scale parameters to measurable quantities develops a rigid geometric structure—a thin “ridge”—along which many different models produce nearly identical experimental signatures. We show that the sharpness of this ridge depends on the absolute neutrino mass scale and has a stable interior maximum, which selects a preferred mass scale without invoking priors or cosmological assumptions. The same geometry explains why the Dirac–Majorana distinction is generically undecidable: the Majorana-specific observable relevant for neutrinoless double beta decay typically lies along the ridge and does not lift the degeneracy, becoming informative only in a small cancellation regime. More generally, we show that the persistent invisibility of heavy neutrinos reflects structural limitations of the observable map and identify which types of measurements can, in principle, overcome them.