Here is what I think regarding on how many cores there are. Originally, I thought there were 5 cores, but the math to it would be off. if 5 Cores = 100%, then 50% = 2.5 Cores, and 10% wouldn't need a whole Core (alternatively, it could be called 20% Zygarde to utilize a whole Core, but it's officially called 10%, and one Core can transform to 10%, so therefore it's not logical for 10% to utilize a whole Core). The math doesn't add up if there are hypothetically five cores. I believe due to the perfect forme's chest-plate revealing the colored hexagons, there will be cores of the five colors: two blue cores, two aqua cores, two white cores and two orange cores since we know that the blue core exists. So 10 cores total with two of each color.It can also be speculated that team flare already has one set (or at least knows the location of one set as indicated by the first episode of XYZ). I also believe that each core is able to manifest a 10% forme as well meaning, there will be 10 individual 10% formes possible as well as different colored ones (blue, aqua, white, orange) in addition to the red one that we already know. Five 10% formes (one color set) will get together to form one 50% Zygarde, while the other color set forms the other 50% forme. Then, the two 50% then join to form complete. The math works perfectly here: (10 x 5) + (10 x 5) = 100. This is also hinted in the opening of XYZ where you can see the gang facing off against team Flare with a 50% zygarde on their side. For the design of 50%'s, it has no other color in it except for the usual green and black color scheme. While it has white in it's right eye, I'm thinking it could be how the core's eye work out, as it does has a normal right eye, and it's left one is not. They could have put something in it's chest, just like they did for the 10%, but they didn't. It could also be the fact that the 50% has 5 frills.
How Zygarde triggers it's Complete form is shown in this video from the Japanese Pokémon video detailing all the things in the arcade.
https://www.youtube.com/watch?v=1HOTWCL1KPs
It seems at 1:03, they were explaining that 50% Zygarde's HP was getting low, compared with the other's HP, so that's how that triggered it's complete form, and then at 1:33, the HP went back to full again. So I figured the transformation depends on it's HP.
If you pay close enough attention, you'll see that this game's graphics mimic that of the Main Series games very well. For example, a Shiny Rayquaza is shown in this trailer Mega Evolving, and the transformation sequence
and movements of Rayquaza are almost exact to that of what Rayquaza does in the Main Series games. The graphic for Dragon Ascent also closely resembles that of what Dragon Ascent looks like in the Main Series games.
Now let's go back to Zygarde. In the trailer, you'll see a 50% Zygarde transforming into Complete Zygarde, which it does using a unique sequence of absorbing a numerous amount of green hexagons. So combined with what we know about Zygarde, we can infer something; these hexagons are Zygarde Cells. And how do we know this? Because of what Zygarde does in the anime, as seen in XY&Z Episode 1. Taking the Zygarde Transformation Sequence into account, I believe it is possible that Zygarde's transformation reacts in a similar sense to Mega Evolution and Primal Reversion: It would be an in-battle transformation. Does Zygarde need a held item containing all the cells and cores in order to activate this? Will it work as a key item? We don't know yet, but we will in the future.