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Its like an unscientific test for rocks. 1 is talc, 10 is diamond. The way it works is you try and scratch one thing with another to see which is harder. So if a nail won't scratch it its probably...

I know you said a nail will not scratch it- but I would be interested if you could do other Moh's tests. I know its not scientific or close to exact, but it'll help us figure it out I think.

I know it is trash but the way the edges are cracked seemed similar to yours.

This is an unknown stone but claimed to be charnley forest. Actually is probably Arkansas.
Fracturing looks similar
Charnley Forrest hone natural razor sharpening stone?? - eBay (item 120465549112...

I would be very interested in the results of if you lapped it on a 220, 320, 600 (or some other numbers) grit stone. And please don't just lap length wise, get some diagonal/sideways scratches in...