Assume the mouse is sliding down the surface as described.  The only forces acting on the mouse are gravity, and the normal force from the surface.  If the mouse is about to leave the surface, that means the normal force is approaching zero, and it becomes zero if the mouse leaves the surface.  If the normal force is zero, then the motion of the mouse reverts to projectile motion, under gravity as the only force, where the vertical motion (in this case the "Y")is a squared function of "X".  Given that the initial velocity of the mouse in "X" is extremely small (essentially approaches zero), it's only the normal force on the surface that can supply a component of force to change the "X" velocity, so this fits.  If n=2, the mouse can slide down the resultant curve with zero normal force yet just follow the surface

Max "n" = 2.  Or I suppose n= I, lim I-->2