Bohr Model of Hydrogen
The non-negative integer $\, \hat{n} \,$ is called the prinicpal quantum number of $\, \gamma$. We imagine that such a photon could result from an extended history of many emissions and absorptions. We require that these interactions have been coherent in order to maintain consistent accounts. But even given that constraint, phase angles might vary by as much as $\pm \, \pi/4$ radians, and quarks could still be assigned to the same sub-orbital octant. Moreover, particles composed from the same quarks may have different phase angles if only because the initial phase angle $\, \theta_{\sf{0}}$ is arbitrary. Accordingly, circular bundles can be distinguished from each other by their phase angle, and $\, \hat{n} \,$ is not constrained by Pauli's exclusion principle.