The Gallium Anomaly in the Cosmological Thermosynthesis Theory v3.2: Entropic Neutrino–Etherion Couplings and Falsifiable Predictions

The Gallium Anomaly—a persistent ∼ 20% deficit in the electron neutrino capture rate observed in 71Ga calibration experiments with intense 51Cr and 37Ar sources—represents one of the most significant tensions in neutrino physics. Within the Cosmological Thermosynthesis Theory v3.2 (TTC v3.2), this anomaly is not an indication of sterile neutrinos but a directconsequence of entropic couplings between Standard Model neutrinos and the primordial etherion superfluid, composed of ultralight scalar bosons with mass me = (1.00±0.05)×10−22 eV. We derive a rigorous mathematical framework wherein the effective neutrino mass receives corrections from the local etherion density and configurational entropy, yielding a modified capture cross section that quantitatively reproduces the observed deficit. Recent results from the BEST experiment (2022–2024) and updated global fits strengthen the case for this interpretation. All definitions specify domains, codomains, hypotheses, and functional spaces; lemmas, propositions, and theorems include explicit hypotheses and formal proofs. The framework yields falsifiable predictions for DUNE, JUNO, and next-generation gallium detectors, positioning the Gallium Anomaly as a critical empirical test of TTC v3.2’s unified neutrino–superfluid dynamics.