Alright, this three timeline thing makes perfect sense to me and I will explain how it fits together in my mind. I didn't read the entire topic so I don't know if someone else posed the same reasoning, but here we go.
OBVIOUS SPOILERS
During the course of the Ocarina of Time, there are four times Link must travel through the past in order to progress through the game. This effectively creates five separate timelines (each time travel action moves Link to an entirely new one).
Let's start with the two obvious ones and then explain the three others:
1. Link defeats Ganondorf and disappears. This is the timeline that is devoid of Link immediately following the defeat of Ganon because Zelda sends him away to a different timeline where he can live out his childhood. This timeline explains why the opening sequence of WW says the Hero of Time mysteriously disappeared and didn't come to the aid of Hyrule when Ganon attacked once again.
2. Link is sent back to his past to relive his childhood. With the knowledge of his future defeat of Ganon, Young Link informs Young Zelda and Ganon is arrested before he has a chance to spring the attack. Link then goes on to experience the MM events.
3. The first time Link pulls the Master Sword out of the Stone. This action removes Link from that specific timeline. Link is gone forever and Ganon is free to do whatever he chooses. Hence the left timeline.
4. Link is unable to conquer the Spirit Temple. He puts the sword back in the pedestal and is removed from the current timeline. Ganon would remain undefeated.
5. Link pulls out the Master Sword after accomplishing what he needs to in the Spirit Temple. Same outcome as number 3.
Timelines 3, 4, and 5 are all abandoned after Link travels to a different timeline. In each of these scenarios, Ganon wins and Hyrule is defeated. The only difference from timelines numbered 4 and 3/5 is that in timeline 4, the temples up to the Spirit Temple are conquered. This does not matter in the grand scheme of things. Therefore, timelines 3, 4, and 5 can be combined. Thus leaving the three timelines illustrated in the diagram.
I realize that it may be necessary to travel back and forth in time to complete the Shadow Temple/Well of Truth, but it would lead to two abandoned timelines equivalent to those explained above. It's also possible to beat the game without the Lens of Truth, but that's beside the point.
I highly disagree with the theory that the left timeline is caused by a Game Over. Game Overs should always be non-canonical.
END SPOILERS
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