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The diameters can be whatever works. For the ones I build, I normally use a 1/4 x 20 for both the bridge and the nut. I just adjust the depth of the nut slot to get the strings to the correct height.
I run red fish line from tuners to nut to bridge at set up. Use dowel rods for set up...this will determine the string height you want, replace the dowel rods with the varied size of nut/bolt and bridge/bolt....been doing this on several set ups and it works great.....good luck man.......