Pauli, hands on
Three anticommuting spin matrices fit in 2 × 2, one per axis of NRS³; two fermions
never share a state; shells close at 2n². A fourth generator, time, does not fit:
that is Dirac's page. Everything below is computed live.
Spin ½ on the sphere
⟨σx⟩, ⟨σy⟩, ⟨σz⟩ are the three coordinates of one arrow. Drag to turn.
⟨σ⟩ = (, , )
|⟨σ⟩|² =
Exclusion: |ψ ∧ φ|(i, j) on 8 sites
Turn φ towards ψ. The antisymmetric amplitude dies everywhere: two fermions cannot share a state.
‖ψ ∧ φ‖ = = √2 · sin(angle)
Shells fill to 2n²
Each orbital takes one ↑ and one ↓, never two of the same: 2(2l + 1) per subshell.
Lean (nrs3-pauli-dirac):
antisymmetrize_self (ψ ∧ ψ = 0), shell_card (∑ 2(2l + 1) = 2n²),
sigma_mul (σxσy = iσz), no_four_anticommuting (no fourth in 2 × 2).
Shell numbers are
capacities, not the lengths of the periods of the table.