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Nope, the work horses are the 1 & 8K the 12k is a great finisher, but you should be getting great edges off an 8K.
Your edge does not get straight until 8K, so a 3, 4 or 5k is just a step, either one will work just fine.
I would not use the Diamond Paste after the 12 or 8k and just use the Chrome Oxide.
You could use the Diamond to touch up, if you feel the edge is flagging, then follow with Chrome Oxide to smooth the diamond.
Which Diamond are you using? .50 is aggressive .25 is a better touch up grit. Not all diamond is equal in purity of grit size and performance for razors.
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I have both 1 and .5 micron sprays, both from SRD. My understanding is that 1micron is about 14k grit, so why skip that?
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My progression is: 1k, 3k, 5k, 10k, 12k (Naniwa SS) Crox on leather (or CBN 0.25) and i have a very good result with it.
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I also use the Naniwa Super Stones; 1, 3, 5, 8 and 12. Just added the 3 to the mix and I'm glad I did. An extra stone but much easier than going from the 1 to the 5.
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I get great edges from a 1K,4K,8K,Chinese natural stone and CrOx paddle. A 12k would be nice addition
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"I have both 1 and .5 micron sprays, both from SRD. My understanding is that 1micron is about 14k grit, so why skip that?"
It is not just about the grit size, Diamond in particular is very aggressive cutting and will leave a deep stria pattern and rough edge, especially if used with pressure. You then have to smooth out the edge with Chrome Oxide or Cerium.
So your Diamond may be negating the polishing you are doing with your stones. 1 micron is way too aggressive for polishing, .50 is ok, for refreshing, .25 is better, but still will need a Chrome or Cerium Oxide follow up to smooth out.
CBN is an altogether different cutting paste and leaves a much smoother edge, even with a larger grit, you can shave straight off of a .25 CBN edge.
Try skipping the diamond and see if it improves your edges. Make sure you are using a proven. good for razors Chrome Oxide. SRD, Hand America or Kremer Pigments are pure, Chrome Oxide. Hardware store Chrome Oxide sticks contain abrasives for polishing and will leave a harsh edge.