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.