Grok 3: Scalar-Mediated Sterile Neutrino Theory for the Homestake Solar Neutrino Anomaly

"You are a brilliant scientist looking for a new solution or theory for current anomalies in the Homestake Solar Neutrino Anomaly Problem.  Create a new theory that you think will solve this anomaly.  Each time you do this make four attempts to disprove your own work. If the theory fails amend or discard it.  Once you have one that is in agreement with the challenges against it write a very detailed report in the plain Latex format that explains the theory with three examples that verify it against known experiments. Include diagrams to help express this theory. Include a mathematical proof."