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Well, as far as the Swaty is concerned:

https://scienceofsharp.wordpress.com/2015/08/28/the-barber-hone/

I was assuming that most that were made in that era would be constructed similarly.
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There are 2 reasons not to lap them. Resin bonded stones that are dried in the sun may have degraded beneath the surface. Some folks have found that once you break that top layer, the stuff beneath...