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Skip the 1um. From 6k try .50um diamond then .50um CBN or Chrome Oxide for comfort. Chrome Oxide is fine for maintenance, even daily stropping, though not needed, daily.

If you want a bit more...

Yea, about the same grit size.

But diamonds will finish differently, than a stone. 1um diamond will cut more aggressively/deeper than a 14k grit stone.

So, while the grit size may be the same...