Golden-Scaled Triadic Vacuum Dynamics: A Phase-Coupled Star-to-Delta Model

This article develops a mathematical and field-theoretic model of triadic phase dynamicsmotivated by the WUCC–BVP framework. It investigates whether a three-component phasecoupled system exhibits distinct equilibrium and dynamical behaviour when its interactiontopology transitions from a central star network to a closed triangular loop, and whetherGolden Ratio scaling produces measurable residual effects. A specified golden-weighted complex sum yields an exact normalized magnitude of √2/φ and a phase of approximately37.761◦.To move beyond phenomenological ansätze, we extend the framework into a dual-sectorGinzburg-Landau field theory, coupling binary conjugate sectors (Ψ+,Ψ−) with a goldenamplitude asymmetry ratio (ρ+/ρ− = φ2). We derive the Euler-Lagrange equations, analyze scale transformations via Derrick’s theorem, and establish stability criteria for localizedtopological excitations and persistent circulation currents. Finally, controlled analogue experiments are proposed to test the model without assuming that its interpretation of thephysical vacuum is a priori correct.