Triune Harmonic Dynamics as a Basis for a Scalar Field Model of the Universal Equilibrium Point

Abstract: We present an integrated model in which Triune Harmonic Dynamics (THD) provides the mathematical and physical basis for a "Universal Equilibrium Point" — a unique fixed point in a coupled tri-layer system. The model uses the equivalence of the KL-barycenter mode and the minimum-action state as its core principle. To address potential critiques, the model's parameters are anchored to the previously published THD ranges. It also adds robustness beyond Gaussian assumptions, quantifies sensitivity to a coupling strength parameter ($\eta$), and provides quantitative, falsifiable predictions for experimental testing. These testable channels include atomic interferometry, fifth-force effects, and gravitational wave signatures. In a time where understanding stability within complex, multi-layered systems is critical to both science and society, this framework offers a pathway to identify and maintain states of natural balance with precision. The document includes appendices with figures showing layer distributions and the convergence of a gradient descent algorithm to the equilibrium point. Keywords: Triune Harmonic Dynamics, Scalar Field, Quantum-Gravity, KL-barycenter, Minimum-Action State, Universal Equilibrium Point, Falsifiable Predictions DOI: 10.5281/zenodo.15686919 Additional Information: Methodology: The paper demonstrates that the KL-barycenter of three convex, coupled distributions yields a unique point $z^*$ that aligns with the THD cycle. Key Equivalence: The primary novelty is the explicit use of the equivalence "KL-barycenter mode = minimum-action state". This connects information theory and physics, providing a new way to interpret statistical centers physically and enabling cross-pollination of methods. Testable Predictions: The model provides specific readouts for experiments, including a predicted phase shift in atomic interferometry, a fifth force with a specific range, and gravitational wave sidebands and high-frequency strain components. Robustness: The paper discusses the model's behavior beyond Gaussian assumptions, considering factors like skewness, tails, and multimodality. It argues that even with these complexities, a unique global maximizer can often be restored.