Quote from: TPTB_need_war on October 30, 2015, 01:58:47 PM

Consistency in our case is the probability of a double-spend (and the inability to reverse a record of a completed transaction, which is involved in the same probability), since that is the only consistency that we need. Consistency of topology seems to be irrelevant as a direct metric of any consistency that concerns the goal of the consensus.

Let's start from this point.

I find your definition of "consistency" unsuitable for cryptocurrency analysis. I could create millions different instances of a ledger in such a way that they can be merged into a single instance without a single double-spending at all. Do we see consistency in such the case (before merging)? Obviously, not. Note that CAP theorem is used on a more abstract level than the level of account balances. I can imagine a perfectly consistent distributed system (by sacrificing A and P) which sees all double-spends that have ever happened. If we use your definition of "consistency" then we'll get an absurd result. I suggest to stay away of home-made definitions because they will lead to profanation of Brewer's theorem and won't let us to do a proper analysis.

Once you agree with me on the above we'll move to the next point.