Quote from: caspar.holzinger on December 18, 2013, 10:37:02 AM

For that reason: Is there mathematical proof that trust is an implicit requirement for solving the double-spending problem?

I think such a notion of mathematical proof is not very helpful at all. I trust the other bitcoin nodes run the bitcoin source code I know. There I believe with high degree of certainy that the network will be behave in a certain way. What bitcoin as a network does is deal with probabilities. Bitcoin solves problems in the real world by using concept which are absolutely foreign to modern mathematics, viewed in the traditional way.