Spin degeneracy in filling a one-dimensional well ($g_s=2s+1$)

When spin does not split the orbital energies, a fermionic orbital can contain $2s+1$ particles with distinct spin projections. Fill these complete states in order of increasing energy to find a noninteracting many-particle ground state. Pauli exclusion does not require different spatial orbitals for particles with different available spin states. Imposed spin polarization or interactions can change the filling.