Why is it plausible that Friendliness is provable? Or is it more a matter that the problem is so important that it's worth trying regardless?
There is no clearly defined or motivated problem of "proving Friendliness". We need to understand what goals are, what humane goals are, what process can be used to access their formal definition, and what kinds of things can be done with them how to what end. We need to understand these things well, which (on psychological level) triggers association with mathematical proofs, and will probably actually involve some mathematics suitable to the task. Whether the answers take the form of something describable as "provable Friendliness" seems to me an unclear/unmotivated consideration. Unpacking that label might make it possible to provide a more useful response to the question.
This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.