What do you mean by a mind?
All you have given us is that a mind is an optimization process. And: what a human brain does counts as a mind. Evolution does not count as a mind. AIXI may or may not count as a mind (?!).
I understand your desire not to "generalize", but can't we do better than this? Must we rely on Eliezer-sub-28-hunches to distinguish minds from non-minds?
Is the FAI you want to build a mind? That might sound like a dumb question, but why should it be a "mind", given what we want from it?
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Perhaps "mind" should just be tabooed. It doesn't seem to offer anything helpful, and leads to vast fuzzy confusion.