the Kyber conundrum

If you haven't seen "Rogue One" by now, you might not want to read further, as I'm about to spoil part of the film.

On the sere planet of Jedha, our heroine, Jyn Erso (Felicity Jones), encounters a blind almost-Jedi named Chirrut Imwe (Donnie Yen).* Because he's a Force-sensitive, he perceives the mystically powerful Kyber crystal hanging from Jyn's neck. As Jyn walks away from the stranger, he calls after her: "The strongest stars have hearts of Kyber!"

Imwe is a guardian of the local, now-defunct Temple of the Whills,* and Jedha is a planet on which a major Kyber-mining operation has been established. It turns out that the Empire is using these puissant crystals to power its new superweapon: the Death Star. It's unclear whether the Empire is using the crystals for their inherent Force-power or because the crystals have other physical properties that make them uniquely useful for the Death Star project.

So my question is this: if Chirrut Imwe is suggesting that Kyber crystals come from stars... why is the Empire mining them out of the ground on Jedha?

Granted, this isn't necessarily a contradiction: Carl Sagan, in his series "Cosmos," intoned, "We are the starstuff of the universe." It's entirely possible that stellar material might end up baked and folded into a planet. Nevertheless, I'm having trouble imagining how a Kyber crystal goes from here... to there.

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*Way back in Star Wars prehistory, in the 1970s, George Lucas first used the term "Whills" as part of the title of a fictional document called The Journal of the Whills. The trivia for "Rogue One" is that the Whills—re-invoked for this film—were a race of powerful, Force-sensitive beings. The term "Kyber," meanwhile, is a new spelling of what had originally been "Kaiburr," from Alan Dean Foster's 1978 Star Wars-offshoot novel, Splinter of the Mind's Eye: in that story, the planet Circarpous V (also known as Mimban) is the home of the Temple of Pomojema, in whose sanctum sits an enormous gem: the Kaiburr crystal, which is a mighty concentration of the Force that can magnify a Force-user's power.