No, the purple doesn't come back until sanded again and it will turn brownish grey after a few years if not sooner. If I cut through a piece laying in my shop right now the purple would come right out of it. The OP's sample piece is purplish in the center and that's exatly how purple heart works.
Looking at the end of grain of the OP's piece, for me and without having it in hand, purple heart is the best bet.
A lot of purple heart isn't truly purple to begin with, that's why I have to hand pick it. And looking at that sample further sanding of the face(to much unless you ruin it) may be needed to get to that color. That particular piece may have been sitting a long, long while or it is a poor choice of the purple heart species to get the purple color. But the end grain, which is the thumb print of wood and how wood is identified sure looks closest to the purple heart. Pictures only tell us so much though. SO exact identification is tough.
Honduras and genuine Mahogany both look like this and its very light in weight, this exact end grain is the Honduras I believe. There are at least 10 wood species retailers call Mahogany that are not Mahogany at all, not even in the same family:
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