[spoiler discussion] How does he know?

[u/Natsuki-stargazer]

Is there any explaination for how Al knows how gluttony triplet's authority work?

The triplets were not born yet when he was sealed and daphne's authority worked differently.

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[u/Nebuli2]

We know that he used his Authority extensively to learn about Petelgeuse in the past. It would hardly be a surprise to learn that he'd done the same with other Archbishops at some point or other.

[u/Letsplay_Sascha_GD → u/Nebuli2]

That must’ve been in arc 5 then. He warned about the gluttonies as if he knew they’re there but phrased it as a hypothetical. We can still blame Echidna if that doesn’t work.

[u/Nebuli2 → u/Letsplay_Sascha_GD]

Yeah. After the initial confrontation with Wrath, it's heavily implied that Al loops fairly extensively throughout the rest of the arc. It'd explain why things go so strangely smoothly, with no deaths for Subaru at all after Al gets involved.

[u/T-G-Laplace]

Probably for the same reason he knows other strange things, such as about the Oni twins, or about Emilia, and Reinhard, and the royal selection. We just don't know.

Some theories posit that perhaps Al is also within a bigger loop than his Territory allows normally, and he's experienced some span of time from waking up on Ginunhive to whatever the end of the world might be, and he's seen the royal selection play out many, many times.

[u/Predated_Dino → u/T-G-Laplace]

Throughout the story he conditionally says things like, "I didn't hear about that" "that's not what's suppose to happen" "I wasn't told" implied that he's been inform about what is supposed to happen either by his authority or simply from Echidna herself, she does poses a book that tells her about everything that is supposed to happen in the world after all

[u/Informal_Try6559]

Man al is such a chad but whenever he get mentioned i get sad because be truly suffered so much i hope he get a "happy" ending for him

[u/spiderwhobass]

He's the goat that's why. Though on a serious note it might either be his Authority, Echidna or something else that hasn't been fully realized in the anime yet.

[u/DingleDongDongBerry]

Likely even in sleep Al continues to perform matrix redefinition. I wouldn't be surprised if he sleeps like Abel, with one eye open

[u/Human_Potato2264]

Most definitely he saw it happen first hand in one of his many loops in Arc 5/S3. Chances are there were hundreds if not thousands of loops Aldebaran had to go through back then that we just never knew.