Flux quantization in "autistic" magnets

The evanescent electronic wave $\psi$ surrounding an infinitely long cylindrical magnet with rigorously zero surface polarization is explicitly calculated. It is shown that the single-valuedness requirement on $\psi$ entails that the total magnetic flux $\Phi$ is quantized in units $\frac{h}{2e}$ (emu), as there are two (and only two) intercalated ladders of $\frac{e\Phi }{h}:\dots ,-2,-1,0,+1,+2,\dots \mathrm{and} \dots ,-\frac{3}{2},-\frac{1}{2},+\frac{1}{2},+\frac{3}{2},\dots$. A reexamination in this light of our previous argument pertaining to the general "autistic" magnet (that is, the magnet completely trapping its own flux, as is the case with a toroidal magnet) shows that the same conclusion then holds. This conclusion amounts to complete external equivalence of the rigorously "autistic" magnet with the "perfect solenoid" that the superconducting ring truly is (but of course not with the ordinary, imperfect, unquantized solenoid). An experimental test using a toroidal magnet and a rotationally-invariant solid-state electronic interferometer in the Mercereau fashion is proposed.