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I would hazard a guess at 6mm 24 spline, don't recall ever seeing anything different on a Les Paul. Should be simple to take off one of the knobs and check
My son wanted proper gold bonnet knobs instead of the incorrect black ones on his 2018 Jr. No problem, Nick. Bring it over, I have a box full. NOPE!!! Not a single one, [all fit my older pre 2010 Gibsons], would fit. Somethings changed.
Does that guitar have the circuit board mounted pots?. If so, they may be the Bourns ones, every Bourns pot I have run into has coarse spline (18-spline) shafts, making it harder to get correct knobs. You can't use regular U.S. spec fine 24 spline knobs on them, as used by CTS on their pots, which come on most U.S. made guitars. I believe Stew Mac sells coarse spline knobs.
Al