Thanks Tony for pointing that the "stack" the way I've defined it cannot be 31 mm !! It could be a confusion between cm/inches (31 inches is around 78 cm which would make more sense). However, it seems "stack height" can also refer to the "headset" or "jeu de direction".
See here:
"The space a headset takes up is referred to as 'stack height' and tends to be around 42mm. Tange produces a model with a stack height of about 32mm that does the trick if your steerer is just a little bit too short." (
http://bikenstuff.blogspot.fr/2011/08/workshop-convert-your-...The size of the headset obviously has an impact on the "global" stack of the bike ...