The ICCF Ontology of the Inert Neutrino: Deriving Its Mass and Mixing from Causal Saturation

This paper provides a first-principles proof and mathematical model for the existence of the "Sterile Neutrino" based on the Information-Cognitive Compression Field (ICCF) theory. We argue that sterile neutrinos are not additional particles to be introduced but rather a logical extension of the ICCF "compression stability spectrum" in the very low stability region. The paper expands on previously established 3x3 Hamiltonian models for neutrino oscillations and extends them into an NxN matrix, incorporating a sterile neutrino state. We demonstrate that the fundamental mathematical difference between sterile and active neutrinos lies in the fact that sterile neutrinos have zero "transition amplitude" with the standard model leptons due to the complete saturation of their "causal binding". Finally, this framework offers a calculable theoretical path for determining the mass of sterile neutrinos and their mixing angle with active neutrinos.