Mass, Schrödinger Dynamics, and Quantum Field Theory in Static Vibrational Reality

This article develops the mathematical framework of Static Vibrational Reality (SVR). In this view, mass, motion, and dimensionality are consequences of universal phase-locked oscillations. The universal carrier frequency (Ω ≈ 31 nHz) provides a global background phase. The three-dimensional world emerges as the projection of the ℓ=1 triad on the sphere S², while higher multipoles (ℓ=3) necessarily appear through Gaunt algebra and weak nonlinearities. Rest mass corresponds to a rational locking index between the Compton frequency and Ω:ω_C = mc² / ħ = (p/q) Ω + δω_lock, with |δω_lock| ≤ K. By separating the fast carrier from the slow envelope ψ(x,t), the Schrödinger equation appears naturally:iħ D_t ψ = (1/2m)(-iħ∇ - qA)² ψ + V_eff ψ. Quantum field theory is then reinterpreted as the collective dynamics of phase-locked carriers, with gauge fields as Berry connections and gravitation as emergent projection geometry. The framework emphasizes mathematical necessity rather than empirical datasets, and outlines open problems such as triad stability, quantization of the envelope, and embedding of Dirac/Klein–Gordon equations.