Does PDF have some built in data integrity protection that would allow it to repair bitrot to a certain degree?
No. Quite the contrary, data streams in PDFs may be (and often are) compressed using FLATE. In uncompressed content streams a bit flip usually only damages a single instruction or two, often having only an effect on small parts of the page rendering. But in a compressed content stream it usually damages all instructions starting at the flip. If this happens early in the stream, the whole page cannot be rendered anymore.
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