What's your point in quoting that? She's telling the Chief she's mostly in the ship, which is being destroyed, that backs up what I said.

: To me there's plenty of room for her to exist in some form, and/or be rescued
: in some manner. It even smacks of someone making the effort to give their
: life for someone else, going through the whole goodbye speech in a noble
: action, only to be rescued at the last possible second from absolute death.

That didn't happen though. She was already on her way out, she did some kind of seemingly harmful copying thing, she talked about what the Chief would face without her, and then she faded away, and the ship she was in is now rubble. There was no indication of there being any chance or any hope of her continuing to exist in any meaningful way. We were shown her death-- not her impending death, her actual death. I cannot imagine a more thorough and final way of showing it that doesn't require things being vaporized and/or someone who's an expert saying "He's dead, Jim She's dead, John".

: Is that a cheap way out?

Yes, that's why it's bad! Any justification for her returning would be after the fact and hollow. There might be things in the universe that would allow for it but those were not acknowledged by the story in question.

: Many stories do that, because the point of the story isn't "kill with a self-sacrificer"
: so much as it is demonstrating love that would give its own life, and love that would
: go to the end of the earth to save a life, ultimately giving a happy ending.

Yes, and Halo 4 was not one of them, it was clearly about someone-- Cortana-- dying, and someone else-- the Master Chief-- trying to help them (along with some Saturday morning cartoon villains because, what, are they going to pin their story on touchy feely interpersonal stuff? but I digress), and the ultimate failure to help in a meaningful way is so important to that story. That story ended, and it did not have a happy ending.

: There are many styles of stories that use this progression. Halo could go
: a few ways. But my weight is going on Cortana NOT being lost forever;
: again, precisely because the two primary characters are a duo and their
: relationship has been the core of Halo, along with the exploration of the
: concept of the Smart AI, in contrast with human life.

One of the most important contrasts between human life and Halo's human-produced smart AIs is in the life cycle-- AIs have about 7 useful years, then they go rampant, then they cease to function. To contradict that is to render moot at least some of the exploration you say you want.

: Your objective factual statements that there is no way it could possibly be
: true is quite subjective :P

The point isn't to make an absolute statement about the universe. The point was to say that the story was clearly about her death, and about the finality of it, and it offered nothing contrary to that.

: What I see are many plot mechanics and openings for Cortana to continue to
: exist or be returned to 'life' in some manner. Just because there was an
: emotional farewell doesn't mean it is and must be the end.

Yes, they can use a plot device, they can use a deus ex machina, but they always can, and being attached to a character doesn't mean they should. To go back and say now "but then everything turned out OK" is... wrong, I can't come up with any more words for it, it would be wrong.