Three-Plane Scaffold: Numerical Field Data — Borromean Junction and Dirac Zero Modes

grid_x.npy 1D array (80,) of grid coordinates in units of delta. Used as the common axis for all three spatial dimensions. phi_approx.npy (80,80,80) float64. Product-ansatz Borromean junction field: phi_approx(x,y,z) = tanh(x)*tanh(y)*tanh(z) The starting configuration before relaxation. phi_exact_inner.npy (80,80,80) float64. Allen-Cahn relaxed Borromean junction field. Obtained by gradient-flow relaxation of phi_approx under: Delta(phi) = phi*(phi^2 - 1)/delta^2 with Dirichlet boundary conditions. This is phi_exact as used throughout the scaffold programme. The Milnor linking computation should be performed on the zero-sets of this field. phi_exact_full.npy (80,80,80) float64. Earlier version of phi_exact (slightly different relaxation parameters). phi_exact_inner.npy is preferred. phi_relaxed.npy (80,80,80) float64. Intermediate relaxation state. delta_phi_inner.npy (80,80,80) float64. Difference field: delta_phi = phi_exact_inner - phi_approx The correction to the product ansatz. epsilon_0 = ||delta_phi||/||phi_approx|| ~ 1.9%. ZERO MODE FILES---------------psi_x_zero_mode.npypsi_y_zero_mode.npypsi_z_zero_mode.npy (80,80,80) float64 each. Jackiw-Rebbi zero mode amplitudes along each coordinate axis. psi_i(x,y,z) is the amplitude of the Dirac zero mode localised on the i-th domain wall. These are the 1D zero mode profiles extended to 3D. DIRAC COMPUTATION FILES-----------------------dirac_evals.npy (8,) complex128. Eigenvalues of the 3D Dirac operator near zero, computed on a subgrid of phi_exact. The two smallest have |lambda| ~ 4e-8, confirming near-exact Jackiw-Rebbi zero modes. dirac_evecs.npy (n_dof, 8) complex64. Corresponding eigenvectors. dirac_xsub.npy 1D array. Grid coordinates for the subgrid used in the Dirac computation. Papers: https://doi.org/10.5281/zenodo.19267506 https://doi.org/10.5281/zenodo.19202565 https://doi.org/10.5281/zenodo.19301348