[javert]

It's hard to downvote a thoughtful comment from a smart person, but you're just plain, flat out wrong.

Bitcoin is a heuristic for Byzantine concensus that requires 50% + epsilon of mining hash power to subvert.

This is not explicitly stated in the original paper, but the original paper comes very close.

I don't know what else you would want.

Regarding economics: All you need for a functioning currency is a supply of speculators who will bet on its future value and thus prop it up. That is only sustainable if the currency is the best at what it does for some meaningful niche (e.g. untrusted digital transactions). This is not part of any proir school of economics, but it's close to common sense, and is strongly supported by the success of bitcoin thus far.

[betterunix]

You are already giving an unclear definition when you use terms like "mining hash power." What rigorous definition can you give for that term? What sort of model of computation are we working with (or is the definition based on information theory?)?

For comparison, consider the definition of security used in this recently published paper:

http://eprint.iacr.org/2013/443

The definition is long, but very clear. Probabilistic polynomial time Turing machines are used as a model of computation; the adversary is given more power by being allowed to be non-uniform (i.e. the adversary can be a different machine for different security parameters). The security properties are clearly defined in terms of this model of computation, and a construction is given and proved to meet the properties (under certain hardness assumptions).

Note that there is no possible way that Bitcoin could meet the security definition given in that paper, because that definition requires the existence of a bank that issues the cash. This is true of previous work on digital cash as well, including the work that preceded Bitcoin. That is why it is necessary to develop a security definition that makes sense for systems like Bitcoin -- digital cash systems in which there is no bank. That is the complaint I have: no satisfactory definition has been given.

"This is not part of any proir school of economics, but it's close to common sense, and is strongly supported by the success of bitcoin thus far."

Economics often defies common sense, so I would be wary of using common sense as the basis for a currency.