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Before you do anything make sure you're tuning it correctly. I only say this is because I recently discovered (30 odd years later) that I was doing it wrong.
Always tune up to pitch
Order is d, g, a, b, E, e
Once the D is in Pitch, give it a stretch the length of the string and tune it back up to pitch. Repeat this process until the stretch doesn't change the pitch.
Repeat for each string in the order described.
If that fails check the angle of the nut. The strings should be rising to the Head side of the nut and coming pretty much straight off the fretboard side edge.
Also check the saddles and in particular the G. Use a magnifier if you have to and look for any etching or burrs in the aluminum that could affect the string.
If it's scenario one problem solved, either the nut or the bridge though, if it were me I would take somebody I trusted. That said Joe Di Cola does a series of videos on YouTube that'll walk you through setup.
And so...after having a bone nut installed....in Nashville.....I feel there is a positive tonal difference.....but, there is more of a G String tuning issue than previously experienced with the 2019 R8 nylon nut. Yes, I use nut lubricant. The Strings have been on a good while...two months...
The slot is too narrow- widen it- and don't bother changing the nut
I've had great success by putting pencil lead (graphite, actually) in the slots at the nut. It looks messy at first but it cleans up.
Seriously, take the string out of the slot and just scribble the pencil in the slot. Get plenty of graphite dust in there so it's good and slippery. Put the sting back and you're good to go!
Definitely the nut. You can definitely widen the nut slot, but I've replaced a few CS poorly cut nuts causing tuning stability issues with a quality bone nut and the tuning has been rock solid ever since.
As others have said, have a luthier check the nut slots to be sure they're filed correctly and also lubricate them every time you do a string change (pencil lead works great, but there are other products out there such as Big Bends Nut Sauce). You can also lube your saddle slots.