It's really easy to figure out.
Your Objective lens is 56mm, lets assume its 1mm wider for the actual tube metal. Thus a diameter of 58mm.
The radius of that is then 29mm, which converted to inches is 1.14"
So, with a totally flat surface, the minimum ring height would be 1.14". (Because ring height is measured from rail to center of mount)
Because the AX has a single rail, and hopefully your surgeon lines up with this, that is the applicable minimum ring height.
If you want to fit Butler Creeks etc then you need slightly more height.
I am assuming your Scalpel, like all others has 20MOA built in so you don't need a canted mount, and the scope has 120MOA anyway, so you will have plenty adjustment.
The ATACR is a 34mm tube and you will be mounting to picatinny so that gives you these options:
SP4001 (1.18") This is the lowest that will fit but there will be very little clearance, not enough to get a Butler creek on.
SP4006 (1.34") This should be the lowest whilst retaining adequate clearance for scope caps and any mis-measurements
SP4002 (1.46") High. I have these to enable me to be closer in line for NV Equipment, you need to raise the cheekpiece about 13-15mm to see properly.