Thanks all for your suggestions which led me to the Home Depot where I found a thing called a "Grinding Disc with Type 27 Depressed Center". The depressed center allows for flush grinding of a part against the face. The dimensions are wrong for my mount (and I would never do grinding on a lathe or mill) but maybe that's what it's for. I think the mystery is solved.
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I got this in a box of Atlas 618 lathe parts. The shank is 1/2" straight. The circular face is concave and the piece that screws into it is convex.
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