I have a lot to say, but I want to wait until all information is available to be sure. Too many people are jumping the gun with theories before we have the translation. Though from what we've seen so far I highly suspect that the explanation for the third timeline will be totally unsatisfactory and leave a lot of gaps. Even the explanations so far, for things we COULD infer reasonably from the games, are very sparse and bare-bones, and require a bunch of speculation to make any sense. And this is something they've never even hinted at before.
I do want to get in on this naming stuff before we get something shitty. At first I was thinking Downfall Timeline or something, because I remembered seeing that as one translation of that section of the book. But really, I suppose Classic Timeline would suffice.
Edit: OH! Better one: Imprisoning War Timeline.
The three timelines are:
Period of the Hero of Time (Child Era)
Period of the Hero of Time (Adult Era)
Period of the Decline