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This article provides a rigorous mathematical formulation of the oscillatory jets observed in the interstellar object 3I/ATLAS, as captured by Hubble Space Telescope images on December 12 and 27, 2025, within the Thermosynthesis Cosmological Theory (TTC) (Fernandez, 2025). The jets, exhibiting relative brightness variations and structural changes indicative of rotational oscillation or source variability, are modeled as emergent phenomena arising from entropic fluctuations in a primordial superfluid of etherions, ultralight scalar particles with mass me = (1.00 ± 0.05) × 10−22 eV. All definitions specify domains, codomains, hypotheses, and mathematical spaces. Lemmas, propositions, and theorems are numbered with explicit hypotheses, and proofs are fully formal, justified by prior definitions, axioms, or cited results. The framework derives jet oscillation periods consistent with observed 16-hour variability, resolves anomalies such as sunward anti-tails through etherion-fermion couplings, and yields implications for cyclic cosmology, including baryogenesis enhancement via jet-mediated panspermia and falsifiable predictions for gravitational wave signatures (LIGO) and neutrino oscillations (DUNE).Additional hypotheses, such as compactness of spatial manifolds for integral convergence, are declared; without them, results may fail, as illustrated by divergent integrals in non-compact spaces.