Geometric Seesaw and the Order-Parameter Origin of Neutrino Masses

The extreme smallness of neutrino masses is one of the most prominent unsolved problems in the Standard Model of particle physics. The standard seesaw mechanism explains the tiny masses of left-handed neutrinos by introducing right-handed neutrinos at an ultra-high energy scale (~10^14 GeV), but this introduces a new physics scale twelve orders of magnitude larger than the electroweak scale. This paper demonstrates that the Order Parameter Spacetime Theory provides a geometric origin for the seesaw mechanism: the geometric structure of Type-B traversable singularities directly suppresses the mixing strength between left- and right-handed neutrinos. When the electroweak phase transition crosses the Type-B singularity, the metric degeneracy suppresses the geometric overlap integral of the Dirac mixing term, endowing the neutrino mass with an additional geometric decoupling factor: m_ν ≈ (m_D^2/M_R) · (φ_c/φ_0)²ᵖ. This mechanism does not replace the mathematical structure of the standard seesaw but supplies its geometric origin. The lightness of neutrinos is not a coincidence but an inevitable consequence of geometric decoupling at the Type-B singularity. If future neutrinoless double-beta decay experiments measure a neutrino mass outside the range predicted by the geometric seesaw, this theory is falsified.