Geometry Selection of the Absolute Neutrino Mass Scal

The absolute neutrino mass scale is unconstrained by oscillation data and is often treated as a free parameter subject to external bounds. We show that this view is incomplete. By formulating the minimal seesaw as an inverse problem in observable space, we identify a geometric organizing structure—a ridge—associated with a near-null direction of the observable Jacobian. This structure explains the clustering and degeneracies commonly observed in parameter scans. We demonstrate that the sharpness of the ridge depends on the absolute neutrino mass scale and exhibits a stable interior maximum. Requiring such an interior extremum yields a deterministic selection principle for the lightest neutrino mass that does not rely on priors, cosmological assumptions, or kinematic constraints. The same geometric framework explains the structural invisibility of heavy neutrino parameters and shows how appropriate extensions of the observable set can systematically restore identifiability.