Vortex Membrane Field Theory in ℝ⁴: Dynamical Evolution, Projection Mechanics, and Membrane Interactions (QSOL-IMC Volume II)

This record presents QSOL-IMC Volume II, a complete theoretical and computational framework for vortex membrane field theory in flat ℝ⁴. Building on Volume I’s operator, lattice, and spectral layers, this volume develops a physics-inspired model where codimension-2 vortex membranes act as dynamical, soliton-like structures governed by the 4D incompressible Euler equations. The work formalizes: Vorticity as distributional 2-forms supported on membranes Transport under ∂ₜΩ + ℒᵥΩ = 0 Velocity reconstruction via the 4D Biot–Savart operator Localized Induction Approximation in ℝ⁴, yielding Skew-Mean-Curvature Flow (SMCF) Construction and stability of S² vortex solitons Full energy model (kinetic, core, and surface tension contributions) Computation of equilibrium radii and normal-mode spectra 4D→3D projection mechanisms, producing Coulomb-like 1/r effective fields Interaction potentials, including long-range ∼1/d² behavior and core-level exclusion Integration with QSOL-IMC’s Volume I structures (SU(3) operator layer, lattice priors, spectral algebraics) Included files provide:• The formal PDF monograph• Conceptual mind-maps• Infographics and explanatory diagrams• A multimedia demonstration• An observation/derivation supplement• A short conceptual “Particles as 4D Vortex Membranes” audio explanation• The QSOL-IMC Volume II Main reference document Together these materials form the authoritative reference for the dynamical, geometric, and observational structure of the 4D Vortex Membrane Field Theory.