Geometric Origin of Neutrino Mass: The Seesaw Mechanism in the Zhang Effective Metric

The non-zero but extraordinarily small mass of neutrinos remains one of the most profound mysteries in particle physics. While the standard Type-I Seesaw mechanism introduces heavy right-handed neutrinos to suppress the mass, it lacks a fundamental origin for the required heavy mass scale. In this paper, we demonstrate that the rotational-order geometric unification framework naturally provides this origin. Using the Zhang Effective Metric, we show that the coupling between 4D fermions and the internal S³ orientation field generates an effective geometric Seesaw mechanism. The heavy right-handed neutrino mass is dynamically identified with the Kaluza-Klein excitation scale of the S³ fibre, while the tiny left-handed neutrino mass arises from the geometric suppression factor η. This elegantly explains the neutrino mass scale without introducing arbitrary new parameters or ad-hoc symmetries.