  The genuine Kaluza-Klein-like theories--with no fields in addition to
gravity--have difficulties with the existence of massless spinors after the
compactification of some space dimensions \cite{witten}. We proposed in
previous paper a boundary condition for spinors in d=(1+5) compactified on a
flat disk that ensures masslessness of spinors (with all positive half integer
charges) in d=(1+3) as well as their chiral coupling to the corresponding
background gauge gravitational field. In this paper we study the same toy
model, proposing a boundary condition allowing a massless spinor of one
handedness and only one charge (1/2) and infinitely many massive spinors of the
same charge, allowing disc to be curved. We define the operator of momentum to
be Hermitean on the vector space of spinor states--the solutions on a disc with
the boundary.
