Not to insult this important work, but the headline makes this sound a lot more important than it is, although "math proof" should have clued me in otherwise.
I was expecting something that'd actually explain why our planet's core is still hot, without using the thermonuclear crutch, given how it is nearly solid iron (not liquid) at such temperatures; such as properly integrating plasma physics (ie, Birkeland currents) into the math.
The problem is that it's unclear the maths result lines up exactly with reality -- as I understand it, this is that a "perfect scan" lines up exactly with one model of reality. What we want is that some kind of "nearly accurate scan" produces a "nearly accurate reality". From my (limited) reading, the proof doesn't seem to demonstrate that (maybe I scanned it too quickly)
I agree that's a limitation of the proof, but this is a thread about journalism tone. What alternative headline would you or the OP prefer? How much weaker does it need to be? Is "could theoretically help" weak enough, or do we need to go all the way to "could hypothetically, maybe, possibly help"?
Forgive me, but it's frustrating to see Monday morning quarterbacking on a huge, important result that was the culmination of decades of work by the authors. Prior to this, the most general result in boundary rigidity was https://arxiv.org/abs/1205.6425, which only works on simple metrics.
I was expecting something that'd actually explain why our planet's core is still hot, without using the thermonuclear crutch, given how it is nearly solid iron (not liquid) at such temperatures; such as properly integrating plasma physics (ie, Birkeland currents) into the math.