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salad-
I could say the same thing with longer words if you like. e.g. "the carrier transmits a unique cryptographically signed message to the phone that it uses to change the configuration of the cellular baseband modem to remove the SIM lock".
(I'm a bit unclear on the exact technical details of how exactly the message gets to the phone and whether it's the carrier or Apple that does the cryptographic signing, and so on, but you get the idea)
grams
AIUI the official way to unlock an iPhone is for the carrier and/or Apple to send some sort of code to the phone that flicks a switch in the hardware to unlock it.
So Apple might have a log of which phones they've done that for, but the fundamental unlockedness is down to the phone hardware. Phones that were unlocked from the factory or were unlocked by other means won't be on the list.