Remark: The full vector problem is larger

The $t$- and $z$-components of a rough vector field are untwisted scalars. Each has a logarithmic deficient mode for every $0<\mu <2\pi$. Accordingly, the criterion $\mu <\pi$ concerns the transverse helicity sectors, not essential self-adjointness of the full unconstrained vector problem.

No Maxwell constraint, Proca constraint, compatible apex gauge domain, or spinor Green operator is supplied. Spinors additionally require a spin structure. The spinless matching statement of VIII-ST does not choose one. XI-B's flat de Donder gauge fixing is not a substitute for these missing conical domain conditions CheungVIIIST,CheungXIB.