What is the true Legend of Zelda timeline?

Question

Is the claimed historical sequencing of events as outlaid here in the correct order? This question assumes an in-depth knowledge of The Legend of Zelda franchise.

My understanding of the timeline is this (please correct me if wrong):

I'm just trying to understand the story, so at the β₁ junction Link carries out the events, presumably first, that lead up to the β₁'' junction where he then travels back in time to β₁ to carry out the events leading up to the β₁' junction? Do I have that right?

It would just be nice to have a theoretically plausible explanation as to how the timeline could be manifested in such a way that it is inline with the historical storyline of the franchise.

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Here is another rendition of the timeline I made with the help of more clarification from the commenters (Right? Wrong?):

To be clear:

[α-β line]
    -skyward sword
    -the minish cap
    -four swords
    -ocarina of time
[β-β0 line]
    -a link to the past
    -oracle of ages
    -oracle of seasons
    -link's awakening
    -the legend of zelda
    -the adventure of link
[β-β1 line]
    -ocarina of time final cut scene
[β1-β1 loop]
    -adult link from ocarina of time sent back in time
[β1-β1' line]
    -majora's mask
    -twilight princess
    -four swords adventures

[β1'-β1'' wave]
    -yeah, not sure... the official timeline suggest that there was an option to be a child or adult (need some clarity here)
[β1''-present]
    -yeah, just guessing here. 

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Here is yet another rendition of the timeline with further clarification, with the exception of not knowing the structure of events in the purple dotted region:

To be clear:

[ω-α line]
    -skyward sword
    -the minish cap
    -four swords
[α-α0 line]
    -ocarina of time (child)
[α0-α1 wave]
    -ocarina of time (link's hibernation)
[α1-β line]
    -ocarina of time (adult)
[β-β0 line]
    -a link to the past
    -oracle of ages
    -oracle of seasons
    -link's awakening
    -the legend of zelda
    -the adventure of link
[β-β1 line]
    -ocarina of time final cut scene
[β1-α bend]
    -adult link from ocarina of time sent back in time
[α-β1' line]
    -majora's mask
    -twilight princess
    -four swords adventures

[β1'-β1'' wave]
    -yeah, not sure... the official timeline suggest that there was an option to be a child or adult (need some clarity here)
[β1''-present]
    -yeah, just guessing here. 

Notice that this timeline makes the statement that, relative to α, the future sealing of the Ocarina-of-Time Ganon[dorf] somehow changes the way that people live their lives and build their world in the second life of the non-Ocarina-of-Time Link's world. And, also, this would mean that the non-Ocarina-of-Time Ganon[dorf] remembers the Ocarina-of-Time events because somehow time travel doesn't undo the seal. Right?

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Universe 1:

Universe 2:

Pretty Version:

Answer 1

Your fork is (sort of) in the wrong place.

The child-success path is created in the final cutscenes of the game, when Ganondorf never rises to power.

The adult-success path is the timeline in which you played through at the end of the game, before that cutscene.

The failure path is essentially a do-nothing path, and occurs mid-game. I generally think of it as occurring in the adult timeline, since otherwise it's indistinguishable with the other paths due to ancestry. It occurs any point when Link has to travel back to the past and do something; the future he leaves has been abandoned to Ganondorf's rule. The alterations made while temporarily in the past fork the timeline and result in returning to a slightly different future, where the adult-success timeline occurs.

Answer 2

As far as I know, no. There are multiple problems with this idea, but I guess the biggest problem is the timeline leading up to the very first games.

These require Link to fail in Ocarina of Time. But by doing so he won't be able to travel to the future for obvious reasons. Before failing, this future doesn't exist. Cloning is no solution since that would explain away everything and it's not really different from reincarnation (official timeline explanation).

In addition, there are other problems, just a few examples:

• Link is growing up in several games, not knowing about him being a hero.
• Link almost never starts with his equipment. He doesn't use SkyNet travelling naked, right?
• Several games mention the main characters being reborn throughout history. This might be perception by commoners, but even Ganondorf explains this once (not sure if considered canon since I think it was cut content from OoT).