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It's just the same piece we've already seen, which was procured from the actual organization 'NASA'. Again, it doesn't have any further significance than it came from the moon
and Tsukasa wanted it, and Tokiko made it happen.
To be honest... Anyone thinking it's been on Earth with Tsukasa since before the modern era needs to remember we didn't have the ability to preserve it using the equipment in the Estate before the modern era. And she's been conscious and moving around this whole time for the implied over a thousand years just fine (we've been given plenty of clues to suggest as much at this point through the splash pages and otherwise up to this point). It can't be connected to her in any supernaturally significant way. It's just a rock. A rock from a place humans have only visited six times, as stated in the manga itself around when we learned about the rock, but it's still basically just a rock.
It's kinda silly watching people get so excited over the damn thing.