Schematic representation of caustic structure shortly after shell crossing. (A) Left: schematic representation of a 3D Eulerian caustic shortly after shell crossing along the x-axis direction, together with a 2D slice with y = y₀ (light red plane). Right: Intersection of the caustic surface with the slice (red curve), also shown in the left panel. (B) Schematic representation of the x component of the Lagrangian coordinate, q_x, as a function of the Eulerian coordinate, x, for fixed (y₀, z₀) (solid blue line). Given x₀, the solution of the three-value problem x(q_x) = x₀ is given by q_x, n(x₀, y₀, z₀) for n = 1, 2, and 3, as in Eq. (41).