When the player opens the Reinforcement window, available Armies appear in the vertical window, each with a number inside a circle. What does this number actually represents?
At first, I thought it was the number of total Corps assigned to this Army, including detachments and Reserves. However, a few times I have attempted to put my Reinforcement Corps in an Army with 4 or 5 in the circle, only to receive the message that this Army has already reached its max number of Corps.

So, my only conclusion is that it represents, in fact, the number of Active Corps in the HQ stack (excluding Reserve), which can be quite confusing and forces the player to search around to see whether there are slots available to place new Corps.
I'd suggest that, instead, it states the total number of Corps assigned to the Army, including Reserves and Detachments.