Particular boundary condition ensures that a fermion in d=1+5, compactified on a finite disk, manifests in d=1+3 as massless spinor with a charge 1/2, mass protected and chirally coupled to the gauge field

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.