"In 2023, arXiv received a $5 million grant from the National Science Foundation (NSF Grant 2311521 | “Frameworks: arXiv as an accessible open access research platform”). Distributed over five years (performance conclusion: 2028) this grant’s goal is to create a more discoverable and accessible arXiv to advance scientific innovation."
Edit: my mistake. I’ve always heard it referred to as a “state school” which is true given its land grant status and SUNY affiliation, but it is private.
To be fair, the original article (or posts?) makes no effort to assert why he thinks arXiv is in any risk for its continued existence. It's unlikely that Cornell will go away, nor the site they own.
Cornell University has seven colleges, three of which are public, and four of which are private. I'm an alum, but it's been a while, but my recollection is:
Engineering, Arts and Science, Architecture, Hotel Administration
are private, while:
Industrial & Labor Relations, Agriculture and Life Sciences, Human Ecology
accept public funding. That info might be ~20 years out of date though.