I don't know if it is the "thinnest on the planet". But in terms of decks available in reasonable quantities on the mass market, the thinnest is definitely Cartamundi's "Slimline" E7 card stock. As mentioned already, it's used for their Cohorts deck, and Ellusionist has also used it for several other decks like Tinker Playing Cards and Marbles Playing Cards.
The B9 True Linen Finish decks by Cartamundi are very soft, but they are thicker than a regular USPCC produced decks, whereas the E7 Slimline decks are noticeably thinner. I've covered this in an article here:
The Cartamundi Decks: A comparison between their popular finishes
https://playingcarddecks.com/blogs/...s-a-comparison-between-their-popular-finishes
Just be aware that Ellusionist's marketing photos for the E7 deck is somewhat misleading, and they make these decks look far thinner than what they actually are. See this article for a complete exposure of the facts.
False Advertising: An exercise in exposing a misleading product picture
https://boardgamegeek.com/blogpost/91300
The "thin-crush" decks by USPCC have a similar handling and performance to Cartamundi's Slimline E7 stock, but the Cartamundi decks are definitely still thinner overall.