[math-fun] Older & younger versions of our sun

http://www.eso.org/public/news/eso1337/ astronomers tried to search for stars as close as possible to being our sun (same mass & composition), but older & younger. They claim that the sun for some reason is destroying lithium, which might be a resolution of the "lithium problem" which is that there seems to be way less lithium in the universe than big bang models say there ought to be. But surely to make that case one would need evidence that non-stellar material has the expected high lithium content, and that very young stars do too? Where is that evidence? If it cannot be found, the "lithium problem" remains a problem.