It seems that most misundestood my post. Most only thought about the double spending problem in the domain of bitcoin. But my question is more general. ... Finally, if you are not a maths pro, don't comment here.
Perhaps it was a problem with the OP - given this is a bitcoin forum and you didn't properly define the scope as being more general. If you mathematically define the problem, then the question of whether or not there is a mathematical answer may become clear and it will certainly let the mathematically inclined respond.
In short, maybe expecting people to answer a non-mathematically defined problem mathematically is at the root of the answers that you got.
And if you don't want other comments, make a thread that you can moderate. :-)