Possible physical self-asserting of the homogeneous vector potential. A testing puzzle based on a G.P. Thomson-like arrangement

It is suggested a testing puzzle able to reveal the self-asserting property of the homogeneous vector potential field. As pieces of the puzzle are taken three reliable entities : (i) influence of a potential vector on the de Broglie wavelength (ii) a G.P. Thomson-like experimental arrangement and (iii) a special coil designed to create a homogeneous vector potential. The alluded property is not connected with magnetic fluxes surrounded by the vector potential field lines, but it depends on the fluxes which are outside of the respective lines. Also the same property shows that in the tested case the vector potential field is uniquely defined physical quantity, free of any adjusting gauge. So the phenomenology of the suggested quantum test differs on that of macroscopic theory where the vector potential is not uniquely defined and allows a gauge adjustment. Of course that the proposed test has to be subjected to adequate experimental validation.