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“Why/how does polishing compound leave a harsh edge? Wouldn't a smoother (smaller striations) edge be better for your skin?”

Yes, it will polish the bevel, but the abrasives, probably Aluminum...

“I can see the scratches made by my 10000 chinese stone and my strop loaded with car polishing compound takes the scratches off and the edge apears smooth with my glass.
My loaded strop is...