Muon Anomalies and Emergent Fifth-Force Phenomena Within the Cosmological Thermosynthesis Theory v3.2: Etherion–Lepton Couplings, Lepton Flavor Universality Violations, and Falsifiable Predictions for Precision Muon Experiments

This work presents a rigorous mathematical reformulation of muon anomalies within the Cosmological Thermosynthesis Theory v3.2 (TTC v3.2). The persistent discrepancies in the muon anomalous magnetic moment (aµ = (g − 2)/2) and lepton flavor universality (LFU) violations in B-meson decays are reinterpreted not as evidence for discrete new particles but as emergent phenomena arising from etherion–lepton couplings in the primordial superfluid condensate. The etherion field an ultralight scalar boson with mass me = (1.00±0.05)×10−22 eV— induces effective short-range interactions that modify muon propagation and decay amplitudes without violating gauge invariance or introducing ad hoc parameters. We derive: (i) the one-loop correction to ∆aµ from etherion exchange, yielding ∆a TTC µ ∼ 2.5 × 10−9 consistent with Fermilab 2023–2025 results; (ii) flavor-dependent couplings geµµ ̸= geee that reproduce RK = 0.85±0.04 and RK∗ = 0.69±0.11 observed by LHCb; (iii) an emergent “fifth force” with strength α5 ∼ 10−30αG and range λ5 ∼ 1 kpc, testable via precision muonium spectroscopy and atomic interferometry. Integrating recent constraints from Fermilab g − 2, LHCb Run 2, and Belle II, we demonstrate quantitative consistency with TTC v3.2 predictions. All definitions specify domains, codomains, hypotheses, and mathematical spaces; lemmas, propositions, and theorems include explicit proofs. The framework yields falsifiable predictions for upcoming muon g − 2 runs, DUNE neutrino oscillations, and JWST observations of earlyuniverse muon production, positioning precision muon physics as a critical empirical test of TTC v3.2’s unified superfluid dynamics at laboratory scales.