My confusion is that this is just Many Worlds / the Schrödinger equation, and Quantum Darwinism doesn't seem to add anything that wasn't already obvious by inspection. But after reading more, I think that's kind of the point? It's ultimately just an argument for why the Schrödinger equation produces these locally classical regions, plus a bunch of overly flowery prose and dressing up in invented jargon that can mostly be ignored. I think the article failed to ignore that second part and ended up confused.
Many worlds is just the claim that the Schrödinger equation holds in actuality.
I don't think QD makes decisions 'uniquely'. Take this quote,
> The step from the epistemic (“I have evidence of |π17〉”.) to ontic (“The system is in the state |π17〉”.) is then an extrapolation justified by the nature of ρSℰ: Observers who detected evidence consistent with |π17〉 will continue to detect data consistent with |π17〉 when they intercept additional fragments of ℰ. So, while the other branches may be in principle present, observers will perceive only data consistent with the branch to which they got attached by the very first measurement. Other observers that have independently “looked at” S will agree.
Emphasis on "the other branches may be in principle present" — the claim at least in this paper can't be that all branches agree, just that they agree locally.
Without defining what 'actuality' is, then there's no meaning to 'the Schrodinger equation holds in actuality'. In their own way, all interpretations of quantum mechanics claim the Schrodinger equation holds in 'actuality'. Some view probability and potential as a claim on 'actuality'. Others dismiss this and instead view probability skeptically and claim it must thus be true. This is an ontological argument, not a scientific one.
If you don't like the word 'actuality', I can rephrase. Many worlds is just the claim that physical reality materially evolves in correspondence with the Schrödinger equation.
If you want to quibble over what it means for something to be material, go ahead, but unless you can tie it to some specific claim being made about QD I don't really know what the exercise gets you.
