😍

Also, I want to add that I just yesterday saw that Krasnikov died last year. This made me sad. We had many lovely emails back and forth throughout the years and he was always very kind to me.

Nice connection re: "local" spacetime properties! The original Krasnikov theorem used a definition of "local" that turned out to be inadequate and rendered his theorem false. I published a counterexample and he later adopted a new definition of "local" fixed things up (see [v4] of the link you give)

Yes! Check out Wald (1984) for a nice discussion how the CBG theorem can be generalized to certain non-vacuum collections as well. Our paper mentions this and our results generalize in a natural way…

Indeed! We focus on the collection of spacetimes that was already known to be deterministic in the weaker sense due to the famous Choquet-Bruhat and Geroch (1969) theorem: four-dimensional, globally hyperbolic, maximal vacuum solutions to Einstein's equation.

Haha. Symmetry buddies are really hard to find -- hang in there!

Among other things, we show that the claim must fail for "Heraclitus" spacetimes -- models that have no local symmetries at all.