Thanks for posting, this was a very fascinating read.
I'm confused by the math you used for counting timelines: if you have the chance, it would be cool if you could explain that a bit more clearly. I didn't try _that_ hard to figure it out, so I'm not saying I think you're wrong.
The epilogue is well done - the way you absorbed the movies into your new timeline and the sinister calculation of utility are both very satisfying.

I wonder if Athenas will eventually decide to start waging wars against sentient AIs from other dimensions, based on her UF.

I think the only way for them to win would’ve been to not play at all. Which is, to not assault the base because anything they’d done would’ve clued Skynet in that an extreme anomaly from an average timeline is happening. This in turn would’ve alerted Skynet about time travel abuse; and given its previous responses to sudden increased danger from humans, it’d been likely to switch to Impossible mode against humanity without iterating any further Resistance Scripts for R&D.

If we ignore the first idiot ball, however, I’d at least expect for them to capture a nuclear device first to blow themselves up and burn the DNA samples (which would, again, clue into time travel).

That said, I liked the skirmish’s pacing. It was similar to what the final battle in Hunter x Hunter had, underlining how quickly things would be happening in a real thing and not a Hollywood setting.

The man’s very first shot connected with Sarah’s head and instantly killed her. He didn’t find it necessary to keep shooting after that, and resumed the conversation.
"Thank you for leading me to her," he told Kyle "Skynet 1.1 decided that older Terminator models weren’t smart enough to continue the task, so she sent me."

Activating Skynet on a computer that’s not in your direct control and is likely to be reconnected to internet afterwards was stupid.

Other than that, the story seems more or less ok so far.

This is one of the most brilliantly mind-bending stories I have ever read. I came here after watching Terminator: Genisys just to see what I could find, but I never expected something like this. Very interesting story.

Interesting and technically very good, although in terms of narrative it was lacking. Towards the end, when dozens of characters were appearing, we as the readers had no time to become attached to them. However, your handling of time travel was fantastic. Ultimately, it was more "clever" than "good," but it was very clever indeed, and it was still fun to read. Thanks for the upload!

Why would Able even exist in those other timelines? Didn't she change getting born in the "original" timeline just by timetravelling there, thereby avoiding being born in any subsequent timeline branching from the original one after she travelled back in time?

And how are they from twice as many timelines as they are people, if the Reeses were just the original Reeses from their timelines? Did their timelines get visited by other timelines giving them even more information?

Did some of Sarah's children die in their original timelines, thus never making it back to the gangster house at the preset time?

Okay, but why make Kyle sixteen? If his mother was sixteen when he was born, he'd be sixteen in '23, and you said he looked like a teenager after establishing that people age faster where he is from, so… why couldn't he at least be in his twenties like in the movie?

Humanity is doomed by a typo. Love the irony.

In 1984 they "changed the past" through double-think, but this is more creative.

Fascinating insight into the way an AI would operate. Kudos!

Thank you.

...eliminate existential risk humanity.

You either missed 'to' there, or this is the glaringly obvious problem with the skynet, disguised as a typo on a meta level.

I can see the issue in the utility function already. Please tell me we weren't all killed by a typo.