The role of proof of work is to make the creation of information one-way based upon a pre-specified amount of work. Therefore, in a properly constructed system,

The role of proof of work is to make the creation of information one-way based upon a pre-specified amount of work. Therefore, in a properly constructed system, a participant cannot steal the results created by another party. That makes no sense, or the meaning is at least not obvious. What does it mean to make creation of information one-way? Proof of work is just a vote allocation scheme. We want to reach consensus about what the transaction history is and do so by a majority vote and therefore we have to decide who gets how many votes. This alone has no single obviously correct solution, for example, if I have a company with a company account, do I get one vote for the company or do I get a thousand votes because the company has a thousand employees? Or maybe votes proportional to the amount of money in the account? And if the system is anonymous it gets even harder because there is no easy way to know who cast a vote or if someone cast a million votes. And that is the way in which I used identity, the identity of an entity allowed to cast a specific amount of votes. And that is what proof of work does, a collection of mining hardware establishes an entity with a voting power proportional to its hashing power. Identification is generally accepted in the security community to come from something you are (biometrics), something you have (bank card), and [...] An identity is something entirely different from work. Proof of work, since it is one-way, proves that work was performed. This has nothing to do with identity, which cannot be proved by work. As explained above, I was not using identity in the computer security sense but in the sense of the identity of entities with a certain amount of voting power. And all your other remarks essentially also hinge on a misunderstanding of my use of identity, if you read it as entities with voting power it will certainly make more sense.