In effect, regardless of how Coil's power works exactly, both methods are functionally identical to an outside observer (who, in this case, is literally everyone who isn't Coil, including us the readers) and you are merely arguing semantics and philosophy at this point.
Literally the only person this matters to at all is Coil himself and, even then, only from a purely intellectual standpoint.
Both explainations are valid and both require the exact same method to counter them.
So ultimately, the only thing that maters is how you explain it, and the timeline explaination is easier to remember and communicate to others than the simulation explaination.
It's true that it looks the same to us, meaning I don't care if the SI keeps believing that's how it works. However, they way those two powers are written are very different from each other, meaning that if you write the story with Coils power working like that you have to either very clearly announce that it's AU, or you will be spreading misinformation on how Coils power work to the readers, which is how his powers was exaggerated to such a degree in the first place. It also tends to help break the SoD of those who knows that Coil is nowhere near that level of power.
Yes, this is very true. That is why the SI explained it in that fashion. As far as he (and I) knows, it could operate as a true simulation: in a deterministic universe any suffiently high fidelity simulation of a person's actions is a copy of that person.
And even if it doesn't, from anyone who isn't Coil, it looks the same.
And as I stated above, I do not care if your SI believes that's how it works, as long as you make sure that the readers knows that's not how his powers work, because you will spread misinformation, and because I know that it doesn't work like that it keeps nagging me. The only problem I have with the way you described Coils power was that you didn't mark it as the SI having wrong information, and that you defended your view even after I linked the WoG saying that no, Coils power does not work like that.
Edit:
Honestly my reasoning for why it is not a simulation is because that would require a deterministic universe or time-travel. This is because he can use information from the 'dropped' reality in the 'actual' reality before he has determined which reality will be 'actual'. So he is simulating two possible timelines and then everyone exists in the one he chooses in a fully 100% determined reality where even he is unable to take different actions and more doesn't even remember what he simulated until time reaches that point, or he lives one reality and simulates a second until a decision point is reached where he then travels back in time to his previous decision point to decide which timeline is actual.
It's simply much easier to claim he either splits the timeline and drops it, or has the ability to see a parallel timeline, (and the coil in that timeline can see back into his) and whenver he 'drops' a timeline he is either re-merging it, or simply cutting the connection to that coil who then gets to live through that timeline having had the suck dropped on him.
Thats actually a kind of funny viewpoint if you think about all the horrible short or bad lives the alternate Coils get because they weren't the lucky one to have the good life.
Much more likely that the shard sees the future instantly and only feed it to Coil real time after manipulating his choice for the "True" timeline. Occam's Razor and all that.
There's a story about that I think, with the various Coils panicking because he's suddenly in a situation where he's fucked because he got the bad choice.
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