Where does Breath of the Wild take place in the Zelda Timeline

In memory sequence #1 Zelda is holding a ceremony to honour Link and says (paraphrased by memory)

be it skyward bound, through time or in to twilight…

This references Skyward Sword, Ocarina of Time and Twilight Princess, respectively. Thus, Breath of the Wild falls in to the middle timeline split, where the Hero of Time succeeds in defeating Ganondorf and returns as a child.

I believe it might be the Fallen Hero Timeline because the Master Sword is placed in the Lost Woods and it only shows Ganon in the game. It can't be the Child Timeline because the Master Sword is placed in the ruins of the Temple of Time. It can't be Adult Timeline either because it's not in new hyrule, Ganondorf was stoned by the Master Sword underwater,l

There is no definite answer currently. At present, Nintendo has not commented on the placement in the timeline other than saying it is after Ocarina of Time. In the game, there are references to each timeline branch, which makes it quite confusing to sort out.

Others have already pointed out the ceremonial speech wherein Zelda makes references to Twilight Princess, Skyward Sword, and Ocarina of Time, but they've failed to point out some other important pieces.

First of all, the Divine Beasts are all named after the sages from Ocarina of Time (with the exception of the Rito divine beast). This is confirmed in the game's lore for Vah Rutah and Vah Naboris by a stone tablet in Zora's Domain and by Urbosa in a cutscene. Vah Medoh is presumably named after Medli and Vah Rudania after Darunia. But Medli only appears in the Adult Timeline, so the only time where we have all four of these sages is in this timeline.

Also on said stone tablet in Zora's Domain are these words:

It is said that Ruto then awoke as a sage, facing this foe alongside the princess of Hyrule and the hero of legend.

There's now a problem with this being in the Child Timeline. According to Hyrule Historia, the Hero's Shade in Twilight Princess is the Hero of Time from Ocarina of Time. He was never acknowledged as a hero and nothing in the lore indicates Ruto became a sage in the Child Timeline either.

Some weaker, but noteworthy evidence:

Korok Forest:

At Hyrule Castle:

Ending spoiler:

The Resurrection Chamber: The Downfall Timeline is the only timeline where we know Link previously failed to defeat Ganon and died. The Resurrection Chamber might have been created with that in mind. This is also a thematic reason that the game could be in the Downfall Timeline (thematic, meaning it's another story of a hero failing). The Downfall Timeline also has the most appearances from Ganon, and past conflicts with Ganon are mentioned in the game.

The Rito and Korok: Early on before the game was even released, there was a great deal of speculation that this game would be in the Adult Timeline solely based on the existence of the Korok and Rito in game. Previously, these races have only been in the Adult Timeline.

So with this conflicting evidence and more, there can be no definite answer, only theories.

-- Warning: Minor spoilers --

Based on an IGN article (Timeline: BOTW), I believe Breath of the wild takes place on the Windwaker timeline, sometime after Windwaker. I have two theories about when it could be.

1. (Less likely) BOTW takes place after Spirit Tracks, when Ganon manages to find a way to New Hyrule, and due to a long time being on the new continent, everyone forgets it's "New" Hyrule and therefore just calls it Hyrule.
2. (More likely) It is in the Downfall timeline and there is another split in the timeline. At the end of Windwaker, Link and Tetra/Zelda go sailing off into the sunset. BOTW, however, is what would happen if Link fails. This leads to Ganon rising again and uncovering Hyrule from the water. It turns out that the Link and Master Sword in Windwaker were imposters/fakes, and really the Master Sword has been at the bottom of Hyrule the whole time. My main proof for this is that at the beginning of Windwaker it says it has been 100 years and there has been no hero, as Link from OoT had disappeared. At the beginning of BOTW, the "mysterious voice" tells Link that He's been asleep for 100 years. Obviously, it must be the actual Link from OoT, one of Zelda's Descendants, and revived Ganon, without Windwaker really ever happening. (In the official Hyrule Historia Timeline, this would sort of make a branch after Windwaker as another "The Hero Is Defeated".)

Edit: Link in BoTW would have to be the son of Link from OoT (from Malon(?)). This is due to Mipha mentioning how they grew up together, as this Link must have traveled all over Hyrule after OoT with his father. Zelda in BoTW says "Your path seems to mirror your father's", as in to protect the current princess. Notice how most of the Divine Beasts are named after sages from OoT, this was probably the Hero of Time/this Link's father's idea.

Maybe it's some time after the era of decline, where the hero rises and defeats Ganon once and for all.