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As far as I know, the 4001 was designed for low tension flat wound strings with a VERY light core wire...nothing like conventional flats. That was one of the big reasons for the 4003 to be introduced in the first place.

I remember talking on the phone (this was close to 30 years ago!) with John Hall. He said my problem with intonation was the "wrong strings". I thought he was kidding, but when I put on the recommended set, the bass intonated fine and the neck-bowing problem was solved.

Also, conventional flats have equal or greater tension that rounds, so a set of (say) D'Addario flats will put lots of tension on a 4001 neck. A nickel round wound "g" string will have about 38 lbs of tension. The equivalent flat wound will have 51 lbs!

If you have a 4001, please try and use a very light gauge flat (or round, for that matter) string and groom those truss rods gently!