Dimensional Transmutation and the Emergence of the Gluvic Constant Ω

This paper develops the theoretical foundation of Static Vibrational Reality (SVR) by showing that the Gluvić constant Ω ≈ 31 nHz emerges naturally through dimensional transmutation. In analogy with Λ_QCD and the Coleman–Weinberg mechanism, the classically scale-invariant SVR phase field acquires a dynamically generated amplitude, which sets the universal frequency of coherent phase oscillations. This resolves the status of Ω from an empirical parameter to a derived constant of nature. Furthermore, the framework reinterprets the cosmological constant Λ as a consequence of vibrational coherence, thereby offering a unified explanation that avoids the traditional vacuum catastrophe. Empirical evidence from atomic clocks, pulsar timing arrays, supernova residuals, and lunar laser ranging is consistent with the predicted oscillation, while null results in LIGO and weak lensing provide strong model discrimination. The work strengthens the theoretical grounding of SVR and situates Ω alongside established dynamically generated scales in quantum field theory.