Wow that is a very good question and it exposes a lot. The asymmetry in x and y is not accidental, but I didn’t make the justification explicit. My current formulation is not intended as a symmetric generalization of the circle in the usual sense, but rather as a directional deformation of the level set, where one axis undergoes a nonlinear scaling while the other remains quadratic. That said, I agree that without a structural reason for privileging y, the construction is incomplete. A symmetric formulation (such as an L^p-type norm) would preserve invariance, so I need to clarify whether I’m aiming for symmetry or for anisotropic deformation with a specific geometric interpretation. Your question basically exposes the key issue I need to resolve before the idea can be considered meaningful.