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Massless solutions for four coupled first order differential equations forfunctions representing families of spinors on the infinite disc curled into analmost $S^2$ are presented and normalizability conditions discussed. Spinorsinteract with two kinds of spin connection fields of particular coordinatedependence. This is the solution of equations of motion used in "Families ofspinors in $d=(1+5)$ with zweibein and two kinds of spin connection fields onan almost $S^2$".

Massless solutions for families of spinors for the toy model in $d=(1+5)$