Flavor Oscillation via Bulk Leakage: Why Neutrinos are the Only Messengers of the Extra Dimension

We extend the proposed geometric framework to the neutrino sector, addressing the hierarchy problem of neutrino masses without invoking the heavy Right-Handed neutrinos of the See-Saw mechanism. We postulate that while charged fermions (electrons, quarks) are topologically anchored to the 3-brane by their gauge flux tubes ("The Gauge Anchor"), neutrinos—possessing a sterile component—are free to propagate into the AdS5 Bulk. We derive the neutrino mass not as an intrinsic coupling, but as the Higgs Overlap Integral: since the Higgs field is confined to the brane, the neutrino acquires mass only proportionally to the fraction of its wavefunction localized on the 4D manifold. Crucially, we predict a High-Energy Leakage effect: ultra-high-energy cosmic neutrinos have a non-zero probability of tunneling entirely into the Bulk. This manifests as a spectral cutoff in the IceCube data and a specific Flavor Ratio Distortion, as the lightest mass eigenstates (possessing the smallest brane overlap) exhibit the largest bulk leakage cross-section. We define the effective gravity scale M* as the control parameter for falsifiability.