Orbital Dynamics in Variable Mass Systems: Case Study and Transit Prediction for Kepler-167e under "The Great Fading" Hypothesis

This technical paper proposes an observational validation for the The Great Fading (TGF) hypothesis, which postulates a secular decay of stellar mass ($dM/dt < 0$) as a cosmological alternative to Dark Energy. We utilize the exoplanetary system Kepler-167 as a test laboratory, contrasting the standard dynamic explanation for the Transit Timing Variations (TTV) of the gas giant Kepler-167e — attributed to syzygy events (planetary alignment) by Renyu Hu et al. — with the predictions of a variable mass model. While the standard model predicts cyclic and conservative TTV oscillations (zero mean over time), the TGF hypothesis predicts a cumulative delay component (parabolic drift) resulting from adiabatic orbital expansion. We establish a falsifiable prediction for the next transit window estimated for October 2027: the persistence or worsening of the transit delay will constitute preliminary evidence favorable to the TGF hypothesis. This document serves as a theoretical preregistration prior to the acquisition of future observational data.