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 [E. Witten, Nucl. Phys. B 186 (1981) 412; E. Witten, Fermion quantum numbers in Kaluza–Klein theories, Princeton Technical Rep. PRINT-83-1056, October 1983]. We proposed in [N.S. Mankoč Borštnik, H.B. Nielsen, Phys. Lett. B 633 (2006) 771, hep-th/0509101; N.S. Mankoč Borštnik, H.B. Nielsen, hep-th/0311037] a boundary condition for spinors in (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 Letter 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.