I don't know what running "sum on software" means. I don't know what item is being compared to what other item. Are there even two items involved? Are you running sum on an item and later running sum again on the same item?
Because you are running sum on an empty directory, it is clear that you are actually using the directory as input. (As opposed to running sum on the contents of the directory.)
You say "Then our software is deleted, and reinstalled.". You do this because you're not happy with the sum on an empty directory?
A directory entry is a name and an inode number. A directory has many of these. A directory entry is deleted by clobbered the beginning of the name. Directories grow but do not shrink. Two empty directories may be of different sizes. And they may have differents shards of deleted entries laying around. Now put two identical entries in each directory. You may overlay the only differing shard. Or you may still have seemingly identical directories with differing sums.
Because of the tree structure of a file system, there is no legal way to create two identical directories although it can be done through trickery. So I still have no clue as to what you are doing.