Maybe I misunderstand something, or you mean something else, but are you not just seeing the discontinuities in the height you put in? you take the fractional part of the UV x coordinate. That goes from 0 to 1 and then jumps abruptly back to 0.
edit: Oh I see you probably mean something else. Aren’t the things at the red arrows just the edges of the polygons of the mesh? Are you sure it’s shaded smooth?
edit2: I do see the discontinuities when I plug the normal into the base color. But when I just plug in into the normal and set my mesh to shade smooth it looks perfectly smooth, except for the discontinuities in the sawtooth of course.
The bump node layers the normals calculated from it’s input over the existing normals of the mesh. Which are discontinuous.
Setting shade smooth averages the face corner/edge normals to make it smooth, but that happens just before rendering, later in the pipeline.
BTW: wouldn’t this question be more of a ‘support’ question for the #support channel on blender.chat?