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You are right. I was trying to emphasize that, the difference between the 3k, 5k, and 8k before the 12k is the difference on the number of laps and, it's small. You can't go from 200 grit edge to a...

If your 12k is man-made and not a "12k-ish", you don't need anything between them.
You could go for a 8k. Say, after the 3k you need 80-100 laps to bring the edge to the 8k level.
Give your razor...