Stack query - Lattice Library and Expansion Algorithm (X-cost proliferate)
I’d appreciate some help understand how the second ability on Lattice Library interacts with Expansion Algorithm with no other interactions at play.
At the beginning of my turn, [[Lattice Library]] is already on the battlefield with 3 study counters and I cast [[Expansion Algorithm]] for two blue and 7 as my X cost. I choose to proliferate the study counters on Lattice Library 7 times, increasing the count to 10.
Lattice Library sees the first spell with X in its mana cost being cast and creates a 0/0 green and blue Fractal creature token. The token doesn’t enter with +1/+1 counters on it - I need to add those (equal to number of study counters) once it has entered the battlefield.
This is where I’m lost on stacking order. Does the proliferation happen immediately and so the Fractal token sees all 10 study counters and gets 10 +1/+1s or does the creation of the Fractal token get added to the very top of the stack and must resolve, entering the battlefield and then gaining only 3 +1/+1 counters before Expansion Algorithms proliferation can resolve to increase the number to 10?
I’ve an additional query on casting an X-cost proliferation - the final ruling on this card (as per scryfall) is that:
>If you proliferate multiple times, you don't have to choose the same set of players and/or permanents to get additional counters each time.
Which reads to me like, in the example I gave above where X was 7, I could have chosen to proliferate other cards for any number between 0 and 7. I didn’t think this was the case and thought that, if I chose other cards, they also would need to get 7. I thought that proliferation was treated as one full action rather than multiple individual actions, as indicated by two other rules on the card:
>Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.
and
>While proliferating multiple times, players can't respond between proliferating the first time and proliferating the second time, and so on.
Am I misinterpreting these rules? Could I have chosen to proliferate other cards by differing amounts (2, 5, obviously not greater than 7, etc) or did all the cards I chose need to be proliferated by 7 across the board?
Grateful for clarification on both of the above, thanks.