Ok, but which of the two is the true one? What is the root of the tree / hierarch of realities now? You got a diamond topology (like in multiple inheritance) and that is not compatible with a tree, thus inconsistent.
If they are just two copies - i.e. they happen to be identical if they're "copied properly" but there's no causal relationship where one continuously mirrors or copies attributes, behavior or outcomes of the other - then they're just two separate leaves from the "branch" that's running the simulation, there's no diamond topology.
And, of course, they might diverge for various reasons (inherent randomness or intentional tweaks in one of the simulations) at arbitrary time, reinforcing the idea that there's not one entity in two simulations but two separate entities, even if they happen to be identical at the moment, no matter if you run simulations in parallel or sequentially.
In such cases, the question of "which is the true one" is really empty, there's no meaningful notion of trueness, all instances of a similar entity are equally valid. If we'd be making copies of sentient entities, then perhaps we might want to define some distinction to privilege one of the copies over the other (e.g. in mind uploading the physical/original entity over the upload), but if the simulations are equivalent then that distinction between copies/instances is just arbitrary and all of them essentially are just as valid.
> Entities in each simulation are separate instances, no matter if you run simulations in parallel or sequentially
Things can't "happen" to be identical, they are (one). E.g. I write the concept of the number 3 in a hundred different languages, fonts and styles. They are all the same, only their hosting representations are many.
I think our disagreement boils down to whether you accept or reject this.
> "which is the true one" is really empty, there's no meaningful notion of trueness
> simulations are equivalent, then that distinction is just arbitrary
The key difference from the concept of number of 3 is that the entities we're talking about are mutable, with extensive, continuously changing state. If the simulation advances for a microsecond, then the entity is modified (while we'd generally consider it to be "the same" as I consider me the same me as a second ago), and causes it to differ from a paused copy of that simulation. In that regard, IMHO the "OOP" paradigm of "classes/instances" seems relevant, as we care a lot about that internal state and we'd consider instances as same if and only if modifying the state of one is inherently reflected in the other - which is not the case for separate simulations. Or, of course, if they're immutable - like 'the concept of number 3' and very unlike entities we'd like to simulate.
Furthermore, the changes depend on a large number of factors - potentially the whole simulation - so unless we're certain that the simulations are fully deterministic and without any interference (and we can intentionally ensure that they're not), there's no reason why they would stay the same. We should interpret every simulation as potentially bifurcating an exponential number of times, and each simulation explores just a tiny subset of the theoretically possible futures of each entity; and if you have "snapshots" of simulations, then you can explore many possible intervention-based branches from each point, just as we do in our experiments with simulated worlds.
The appropriate analogy is not the concept of the number 3, but a reality of a number like "0.3" that may get represented as 0.30000000000000004 in one simulation due to floating point approximation, and get corrupted by a cosmic ray bit flop in another one - and we're talking about the properties and experiences of these nonperfect instances of simulations (since if assuming the simulation hypothesis, that's the experiences we get and care about), not about the properties of some theoretical concepts that may be the "core of the entity" (e.g. Plato's philosophy) since they're not real unless/until they get actually implemented or simulated, and if the realization does not match the ideal, if there are any differences whatsoever, then the realization is the one that matters.
