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I'm not sure if the photos depict the lights correctly; do you see a greenish tint, even if it's faint from the stone cleaned? It's quite common on CF & LY. Other than that I don't know what it is....

It does indeed, but from the 4th pic, 1st post with the missing big flakes, the Cretan stone doesn't flake/break like this, it splits into two parts very easily.
BUT you can find this kind of...

I think it's novaculite. Now, if it's a Charnley, Llyn Idwal, something from US or even a Turkish oilstone (the pores on the side), I can't say for sure, the colors are strange indeed.
I have seen...