Noether's Theorem: 2D Phase-Space Conservation

Emmy Noether's theorem is the backbone of every field theory, including the quantum field theory used to build the Standard Model: a continuous symmetry of the Lagrangian always implies a conserved quantity. This 2D companion to the 3D Noether's-theorem simulator keeps the identical particle-in-a-well physics but renders it as a pannable, zoomable top-down potential heat-map instead of a 3D wireframe bowl, and adds a diagnostic the 3D version has no equivalent for: a live scatter trace of the orbit's path through (E, L_z) phase space, so a broken symmetry shows up as a streak in a specific direction rather than just a drifting number. It also fixes a stability gap in the source model — an unconstrained anisotropy slider that lets the well turn into an unbounded saddle instead of the promised precessing rosette for much of its own range — by clamping the effective anisotropy relative to the well's stiffness, verified numerically against the unclamped trajectory before shipping.