Rigorous Mathematical Analysis of SPT0418-47 Observations in Thermosynthesis Cosmological Theory

This article presents a fully rigorous mathematical formulation of the implications of JWST observations of the lensed galaxy SPT0418-47 (z ≈ 4.225) for the Thermosynthesis Cosmological Theory (TTC). In TTC, all physical phenomena emerge from a primordial superfluid of ultralight scalar bosonsetherionswith mass me = (1.00 ± 0.05) × 10−22 eV. Every definition includes explicit domain, codomain, hypotheses, and ambient function space. Lemmas, propositions, and theorems are formally stated with explicit assumptions, and all proofs are fully justified by prior results or established theorems. The framework explains the observed maturity of SPT0418-47 including solar level metallicity, PAH molecules, and a companion galaxythrough (i) accelerated chemical enrichment peaking at z ∼ 10–12 and (ii) modified gravitational lensing due to superfluid fluctuations. These mechanisms resolve the Hubble tension, the cusp–core problem, and early structure formation. Crucially, we declare all additional hypotheses (e.g., compactness of spacetime); without them, results fail, as demonstrated by counterexamples with divergent integrals. Falsifiable predictions are provided for JWST, Euclid, and XRISM.