[iambvk]

Here is what the paper says:

Phase 1.

(a) A proposer selects a proposal number n and sends a prepare request with number n to a majority of acceptors.

(b) If an acceptor receives a prepare request with number n greater than that of any prepare request to which it has already responded, then it responds to the request with a promise not to accept any more proposals numbered less than n and with the highest-numbered proposal (if any) that it has accepted.

Important part of the statement is

  ...with a promise not to accept any more proposals numbered less than n...

So, Phase-1 promise is not on the proposer-identity, but on the proposal-number.

[bakhy]

You're right, my mistake!

But it still should not be an issue, since according to what you quoted an acceptor will not reply to a second proposal that bears the same number ("If an acceptor receives... number n greater than...), which means only one of the two proposers can gather the required majority of promises to move to the next phase, and thus only one of the values can end up being accepted. After the crash you describe, there will be only one accepted value the Proposer-C will receive.

[iambvk]

Such assumptions break network request retries and/or relies on proposer-identity, etc.