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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.

When your error bars are a few hundred years or so, the few weeks between “making paint” and “using paint” isn’t terribly relevant.

Well, we can safely rule out the idea that a cave painting was made with thousand-year-old paint.

It's more difficult to rule out the idea that a thousand-year-old painting was restored with usable paint.

From the artists biography.