I hope once the XC dev comes back to talk about the anon system in use you will finally stop trying to push your mixers stealing coins FUD.
You seem hell bent on pursuing your point without any sort of proof or even time to do your own analysis, as I mentioned before in a previous response.
Take the 1-2hr you spend writing your "technically based post and rigorous mathematical equations" and actually do something about it.
First though, follow the guide again and get your anon working like everyone else has.
If you want to take your first baby steps and need a bit of hand holding, I'm sure someone technical in here can talk in laymens terms for you to grasp.
I did manage to send one anonymous transaction (and only one because the things stopped working after this one).
And I can confirm that that I could find transactions that satisfy equation X=Y+R (plus minus transaction fees). The first transaction (that sent X coins) is my original transaction. The second transaction is transaction that sent coins to my change address. You can easily determine both transactions from qt client. I didn't check thoroughly if there are also other transactions that satisfy this equation (but there are probably not).
I won't post details of my transaction here because I don't trust the operators of mixer nodes and they could probably use this information to track me.
But you can do the same thing with your qt client. If the anonymous sending feature is working, then it is about 1-2 minutes of your work.
There is nothing to be "proved" about equation X=Y+R. If you send X coins and the other party receives Y coins, then the mixer must send you back R coins (to change address). If you don't get R coins back, then the mixer is stealing your coins. What is so hard to understand here?
Btw, some bitcoin mixers actually do this. But they hide it in a "fee".