Time displacement, and the alteration of a single linear continuum as displayed in the Terminator films.

How can skynet rise again in the upcoming T3, if judgement day was supposed to happen in 1997, and John and Sarah killed the T-800 chip?
Consider this, if Skynet was made from Terminator technology, and Skynet sent the Terminator Technology back, where did Skynet come from originally?
There had to have been an original timeline where humans were just smart enough to make a Skynet on their own, before time travel futzed it up.

So, the Terminator technology based Skynet in the first 2 movies is actually from an altered timeline.
So, destroying Cyberdyne, killing Dyson, and cooking the 2 chips only eliminates that timeline, and restores the original.
So, Skynet of the timeline of the first 2 films sent 2 Terminators, but the Skynet that arises in T3 just sends the T-1G.
The very fact Skynet arises in T3 in 2000-01 proves it's a different timeline. This indeed goes along with the line "the future is not set".
BUT, a timeline with John Conner with Kyle Reese as his progeneter, existing in a timeline where Skynet arose from the T-800 chip up until he destroyed it, and then not being erased by that act, already indicates that not only was he already in an alternate timeline to begin with, but he created yet another timeline by destroying the chip.
So, if Skynet rises again in T3, he's actually created a new timeline similar to the one that existed before the first timeline changes in T1.
One big problem with all of this.
If there are diverging timelines in the Terminator films, why does Skynet even try to change history by sending Terminators back in time to kill John Conner?
Sending Terminators back to create an alternate world where Skynet wins would be useless for the Skynet who wants to win in it's own timeline.
So, we're back to a changable single timeline riddled with paradoxes.
Or are we?

I have a theory that allows for the changing of a single timeline with no paradoxes.

It involves the very nature of the time machine.
It's a "time displacement", machine right?

What if it doesn't just displace you THROUGH time, but FROM it as well?

We see that it forms a kind of warp bubble around the traveler.
What if this warp bubble contains it's own artificial mini-spacetime?

I think this mini-spacetime bubble surgicly amutates whatever's inside from our universe, thus allowing it to slip through time, and it also acts as a sheild from our timeline, so that the traveler is unaffected by any history changes.

So, from the point of view of our universe, the time traveler is a sort of "limbo man", who springs into existance from the point they materialize in our time, and if their past gets erased by a history change, it doesn't matter because they've been cut off from that timestream anyway.

Sort of like a temporal cut-and-paste.

So, this warp sheild seperation keeps Reese (and thus John) from vanishing if the future war is prevented, because from our reference point, he was born into our universe from his warp bubble.
Matter of fact, he describes time travel as "kind of like being born".

Same for the Terminator.
As I stated at the begining, there must have been a timeline where humans built Skynet independantly in 2002, and therefore the 1st Terminator must originate from that timeline.
But, when his chip is used to build Skynet in 1997, this would make a paradox that the 1st Terminator would then be built by the 1997 Skynet.
But instead, the time-bubble cut-and-paste sheilds him and he springs into existance from his bubble, and is unaffected by the new time-tangeant of the 1997 Skynet.

This can be applied consistantly to the other time displacements in the other films too.

So, IMO this works with the single changeable timeline the films seem to prefer, and works with the definition and demonstration of the time displacement equipment.