I wonder how they know the axe-heads are 4k years old. Carbon dating tells them how old the material is, but how do they know when the head was formed into an axe? The same goes for cave paintings. They can date how old the paint is, but how do they know when it was painted?
I don't think you can date the axe-heads from the material? I assume they date based on objects found nearby and the technique used to make them. Which is also why knowing the exact location is important.