Core FRCMFD-v2 Evolution Equation
[ \Phi(\mathbf{x},t)=A(\mathbf{x},t)e^{iS(\mathbf{x},t)} ] Complex monad field decomposed into amplitude and phase. --- [ \rho_M(\mathbf{x},t)=|\Phi(\mathbf{x},t)|^2 ] Monad-field configuration density. --- [ \mathbf{J}_M=\rho_M\nabla S ] Configuration-flow / phase-current relation. --- [ \partial_t\rho_M+\nabla\cdot\mathbf{J}_M=0 ] Continuity equation for monad-field conservation. --- # Core FRCMFD-v2 Evolution Equation [ i\partial_t\Phi =============== -\alpha\nabla^2\Phi + \beta|\Phi|^2\Phi + V_{\mathrm{env}}(\mathbf{x},t)\Phi + V_{\mathrm{top}}(\mathbf{x},t)\Phi ] Nonlinear monad-field evolution including environmental and topological coupling sectors. --- # Cylindrical Toroidal Form For axisymmetric winding sectors: [ \Phi(r,\theta,z,t) ================== f(r,z,t)e^{im\theta} ] Topological winding decomposition. --- [ \nabla^2 ======== \partial_r^2 + \frac{1}{r}\partial_r + \partial_z^2 ------------ \frac{m^2}{r^2} ] Cylindrical Laplacian with centrifugal...