We all know for basically a fact, that the way the Marauder’s Map was created, was because of the Potter invisibility cloak. After all, wouldn’t you notice a stag, a dog, or rat trying to “sneak” around Hogwarts castle? I sure would! Therefore, I think the only explanation for the Map is that James Potter had the Cloak during his school years at Hogwarts castle.

Er, not trying to be rude, but this really does not make sense nor have I ever heard of this "fact", could you explain on what your thinking is here or cite a source for this?

I have never seen any discussion about a relation between the Marauder's Map and the invisibility cloak, other than that the invisibility cloak does not protect you from being seen on the map