What Exactly is the Electric Field at the Surface of a Charged Conducting Sphere?

In the presently available literature, one finds distinct results for the electric field at the surface of a charged conducting sphere. In most textbooks, only a simple model is presented in which the electric field leaps from zero (inside the sphere) to a maximum value (just outside the sphere), as follows from Gauss's law. For points exactly at the surface, the charge surrounded by the Gaussian surface becomes ambiguous, and this law is inconclusive. In this paper, by treating the spherical surface as a series of rings, it is shown that that field evaluates to half the discontinuity mentioned above, a result which agrees with more elaborate microscopic models.