Atomic Shell Structure as Three-Level Fractal Hierarchy from Cascade Iteration

We identify the atomic shell structure (1s, 2s, 2p, 3s, 3p, 3d, …) as a three-level fractal hierarchy from the cascade: level 1 (principal quantum number n) from the norm tower 5k; level 2 (angular momentum l) from the Pythagorean decomposition at each level; level 3 (magnetic quantum number ml) from the Z4 rotational symmetry. The maximum principal quantum number n = 7 for naturally occurring elements matches the cascade boundary |Re(J)| = 7.