Tracking cherry picks

I need to maintain a few stable release branches in addition to the 
master branch.  Sometimes a bug is found and the fix needs applied to 
multiple branches.  I would like to be able to list what branches the 
fix has been applied to to validate that it went in everywhere it was 
needed, but after cherry-picking the fix from master to the stable 
branches, the SHA1 of the commit is different, and so git branch 
--contains does not think the commit was applied to each of the stable 
branches.

Is there a way around this?  Why doesn't git-cherrypick record the 
original SHA1 it was picked from in the commit?