The solution of a static two-dimensional wave equation in the Gauss-Mainard
i-Codazzi formalism of Weyl-Dirac theory is obtained in terms of the ellipt
ic function with a complex argument. In particular, by double degenerating
the elliptic function, wave-particle duality results. Associating a superco
nducting behaviour to matter, by means of the duality, we find some superco
nducting parameters: B-c2, the average carrier density, the gap energy and
the pair-breaking time. The discontinuities of these parameters for sequenc
es 1/3, 1/5, 1/7,... imply that the quantum spacetime is Cantorian.