square material strange arifacts

I create a material. There are strange artifacts.
Here is the node setup:

Here is an image of the artifacts (squares are wanted, strange lines not):

Is there any way to avoid those strange lines?
Are these lines a bug?
Thank you for you help!

Not sure what end effect you are going for here but is this what you wanted?

If that is what you were wanting, all I did was disconnect the object connection from the texture coordinate to the vector mapping and used the generated connection instead and it cleared up that edge line that was running through that you had going on.

That’s because of the interaction of the round function and the floating point data used in Cycles.

The round node, makes the ‘jump’ at exactly 0.5, but the way floating points as stored in memory, may be something like 0.49999999 or 0.500000001 (it’s very rare to have a pure 0.5 value, unless deliberatly set).
A quick work around is to avoid the use of coordinates where the round should ‘jump’. This can be made by many means, but in your case a simple solution is to set the scale values of the mapping node to something like 10.001 instead of 10.

Thank you for your quick answere! So I just need to add a very small number to x,y,z? That is an easy workaround!

Oh and sorry for the large file sizes! I forgot to unpack an hdri, so it is better to delete the blendfile before someone sues me!