I've just measure my very recently purchased MIJ Tokai SG., which is the best setup I've ever had on a new guitar, and I won't be changing it.
The first fret height is .88mm
Height of nut at
Low E 2.35mm
A - 2.25mm
D -2.03m
G - 1.85
B - 1.77mm
High E - 1.55mm
All the above measurements are from fretboard to the top of the nut, they don't include the nut slot depths