Chapter 48: Multi-Electron Atoms and Shell Structure

Hydrogen admits an exact solution; every other atom does not. The culprit is electron–electron repulsion, which couples all fermionic modes on the fiber T². This chapter develops the multi-electron atom within Category τ, beginning with helium—the first closed shell—and building toward the full periodic table. Shell structure emerges as T² mode saturation: each principal quantum number n supports 2n² co-rotor slots, and the aufbau principle follows from the energetic ordering of T² harmonics. The periodic table itself is a map of T² mode filling, with noble gases marking complete saturation at each tier.