Firstly, I am sorry for the late answer. Secondly, this is not yet possible in therion yet.
I see just one possibility, how to calculate this number automatically. It is to run therion in debug mode and then, using some script, scan output metapost file (
data.mp) for depth labels, calculate the minimum and export it into TeX file, that will be processed in the output file.
It would be worth to think, how such a problems could be solved. May be exporting these numbers to database would be to most proper solution.
S.