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“[…] lots of the people were mean, and most of them were miserable, even the ones with digital watches. Many were increasingly of the opinion that they’d all made a big mistake coming down from the trees in the first place, and some said that even the trees had been a bad move, and that no-one should ever have left the oceans.”
Douglas Adams, The Hitchhiker’s Guide to the Galaxy (Hitchhiker’s Guide to the Galaxy, #1)
It is possible to run code directly inside PDF files, as can be seen with Doom or Linux running inside a PDF file https://github.com/ading2210/linuxpdf
In addition to that can PDF files prepared to trigger security weaknesses and exploits in PDF readers (often Acrobat Reader), to act as an attack vector and run malicious code.
So no, PDF are not safe by design.