Thermosynthesis and the Calcium King Plot Anomaly: A Rigorous Derivation within the Cosmological Theory

This article presents a rigorous mathematical derivation of the calcium King plot anomaly within the framework of the Cosmological Thermosynthesis Theory (TTCv3.2). In TTC, all physical phenomena emerge from a primordial superfluid of ultralight scalar bosons termed etherions with mass me = (1.00 ± 0.05) × 10−22 eV. We demonstrate that the observed nonlinearity in isotopic transitions of Ca+ and Ca14+ arises naturally from etherion-mediated nuclear polarizability corrections to the standard King relation. All definitions specify domains, codomains, hypotheses, and functional spaces. Lemmas, propositions, and theorems are numbered with explicit hypotheses and formal proofs. The framework yields falsifiable predictions for high-precision spectroscopy experiments at the 10 mHz level, while simultaneously resolving foundational tensions in cosmology, particle physics, and quantum chemistry through a single minimal postulate.