The time travel theory to end all time travel theories (Le joke)
I actually think that the defeated timeline is a timeline we all know well, and that is Young Link's quest for the Spiritual Stones. The idea is that everything has to do with what happens after Zelda sends Link back in time. If we look at the timeline as it's written in Hyrule History. When he pulls the Master Sword he goes into the future and creates the Adult Timeline. After slaying Ganondorf Zelda takes the Ocarina of Time and sends him back in time before he went on his quest for the Spiritual Stones; this is the Child Timeline, in which Link and Zelda warn the King about Ganondorf. Now, there is one timeline that is already going in in the midst of this. The timeline where Link had already retrieved the spiritual stones and pulled the Master Sword from the Temple of Time. This timeline is the one I believe to be the failed timeline. This former timeline (the one we played as Child Link in OoT) is still ongoing however there is no Link because Link as we know has been transported to before the events of Hyrule Castle being attacked by Ganondorf.
Nope
The timeline where Link gathers the stones is the same as the Adult Timeline, the difference is a 7-year-long stasis for Link, nothing else, no time travel involved there
There is a interesting thing with time travel, suppose you have a time machine that moves you through time, if you travel to the past, you create a new series of events (depending on your interpretation, this can either create a paradox or a split timeline), if you travel to the future, nothing changes, you just disappeared mysteriously for a while and then reappeared.
Now suppose you have a window of time that allows you to look into any place at any time in existence, if you look into the past, nothing changes, you just gathered information on events passed, but if you look into the future, you could make preemptive measures to ensure that future doesn't happen, this would be as simple as seeing yourself walk to the left in five minutes, then when the time comes walk to the right, thus a paradox is created, since the window should have shown you walking to the right, but if it did, you would have walked left, hence a paradox is formed, the other interpretation is that a split timeline is created, one that is seen by the window, one that you create when you contradict the window
If you analyze these two devices, you realize something, both are the same, the window of time is a time machine that moves information. If you look into the past, you are sending info from the past into the present (forward time travel, no splits or paradoxes created), if you look into the future, you are sending info from the future into the present (backwards time travel, splits or paradoxes are created)
Now, in relation to Zelda, there are two theories for time travel, one states traveling backwards creates splits, the other one states traveling backwards overwrites the future (there is potential for paradox here, like the song of storms) ,they are called by Locke "A theory" and "B theory", however, for reference (the names are not intuitive, I often forget which is which) I will call the first one "SI" (split interpretation) and the second one "PI" (paradox interpretation), a third one will be "FTT" (forward time travel, doesn't cause splits or paradoxes) and I will analyze the time travel through the series
First thing first, Skyward Sword, there are two time travels here, the gate of time and the timeshift stones, the later don't seem to be actual time travel, rather, they seem to change the state of an object based on how it was in the past, they are a window of time to the past, thus they are FTT
The gate of time is trickier, the tree of life puzzle seemingly indicates PI, planting the seed in the past overwrites the timeline by adding a tree, however, this is not definitive evidence, for all we know, it works under SI, and there is a timeline out there without a tree of life (incidentally, since there would be no Link in this timeline, this would be another downfall timeline)
Now on to OoT, first the easy one, Zelda sending Link back, that is clearly SI
Now the hard one, at first glance, the Master Sword time travel is PI, but that isn't definitive, it could be SI, the song of storms, however, contradicts SI, and some variations of PI allow it to happen, hence I'd say it's PI, which is a pity, because if it was SI, then there would be a reason for the downfall timeline, more on that later. To be more in depth about his reasoning, imagine a random Skull Kid comes into the windmill and plays the song of storms for Guru Guru, Adult Link learns the song, then return to being a child, child Link teaches the song to Guru Guru, the skull kid is edited out of existence, as his teaching the song to Guru Guru would be redundant, of course, this assumes a Skull Kid, but this assumed entity could be anything, a fairy, Rauru, the gods, etc. Occam's Razor destroys this, but thing is, once it happens, it just doesn't happen, when since Link teaches the song, the original teaching is removed from ever having existed, hence no teaching the song, hence paradox (bear with me), however, if it was a god that is above time that introduced the song in the first place, then the circular logic can take place, conclusion: time traveling with the MS falls into PI, due to Deus Ex Theoriza, feel free to disagree with my explanation here, but the circular logic taking place in the first place is enough to conclude PI
I haven't played OoA, so I can't talk much there, however, from what I know, everything seems to indicate a similar situation to the tree of life, we do not know what happens when there are changes to the past, it may be that a split is created, hence SI, or the future is overwritten, hence PI
Lastly, TP, there is brief time travel there, but there are seemingly no repercussions from making changes to the past, however, this is very interesting, it suggests PI, every change made to the past was predestinated (these changes that are made, as far as we know, are Zant placing the mirror shard there, and Link going there and retrieving it) and the whole thing operates in a circle, much like the song of storms, hence it's PI, it's shaky and lacks evidence, but there's a little more evidence supporting PI than SI
So, to sum it up
Timeshift stones: FPP
Gate of time: ambiguous, I am inclined towards SI
picking up the master sword in OoT: FPP
putting back the master in OoT: PI
Zelda sending Link back: SI
Oracle of ages: ambiguous
TP's gate of time: PI, probably
If putting back the MS is place in OoT produced splits, then there would be a reason for the DT, Link disappeared into the new split and left Hyrule at Ganondorf's will, there are many theories that propose this, however, putting back the MS seemingly works under the PI, but, if you are willing to forget the song of storms thing, it becomes ambiguous, and you can justify the DT id you choose to believe the SI
interestingly, unless we can see a new split (such as the adult and child timelines that run parallel) or circular logic (such as the song of storms) taking place, it is very hard to conclude either SI or PI, so most time travel is ambiguous
