Does Emrakul's shuffle trigger go on the stack when it goes to the graveyard?

Emrakul, the Aeons Torn has a triggered ability that says 'When Emrakul is put into a graveyard from anywhere, its owner shuffles their graveyard into their library.' This is a triggered ability, but there is a critical timing detail: the ability triggers when Emrakul is put into the graveyard, meaning it actually does briefly enter the graveyard before the trigger is placed on the stack (CR 603.3).

So to be precise: Emrakul does go to the graveyard first, and the trigger does go on the stack. However, because state-based actions and triggered abilities resolve, by the time players could respond, the trigger is already on the stack and Emrakul is in the graveyard. The trigger then resolves, shuffling the entire graveyard (including Emrakul) back into the library. This is different from a replacement effect — it is a genuine trigger (CR 603.1).

The common misconception is that this works like a replacement effect (as seen on cards like Blightsteel Colossus, which says 'If Blightsteel Colossus would be put into a graveyard, reveal it and shuffle it into its owner's library instead'). A replacement effect never lets the card touch the graveyard. Emrakul's ability is a trigger, not a replacement, so Emrakul does enter the graveyard momentarily.

Concrete example: Your opponent casts Surgical Extraction targeting Emrakul in your graveyard in response to the shuffle trigger. Because Emrakul is in the graveyard while the trigger is on the stack, Surgical Extraction can legally target and exile it along with other copies. When the shuffle trigger resolves, Emrakul is gone, so only the remaining graveyard cards are shuffled in.

Key rules: CR 603.1 (triggered abilities), CR 603.3 (triggers go on the stack after the event), CR 614.1 (replacement effects, for contrast). Emrakul uses a trigger, not a replacement effect, so the card does touch the graveyard briefly.