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The content in scholar.archive.org has been indexed in to Google Scholar (and other indices are likewise welcome to crawl the sitemap). There was some content "only" in scholar.archive.org, but now it should basically all be in Google Scholar. We haven't gotten around to describing this publicly, but it was an explicit decision and partnership between the organizations.

Indeed scholar.archive.org does not currently use citation count in search rankings. We have a decent citation graph, which we are working to expose in scholar (it is visible in fatcat.wiki today). Would probably only ever use citation count as a weak boost in search rankings (eg, "any citations at all", "more than 25 citations" as boosts, nothing beyond that), don't want to create too strong a feedback loop influencing future citations.

scholar.archive.org specifically was partially funded by the Mellon Foundation (and partially through donations and other service revenue). IA overall has diverse funding, including grants and service revenue from the USA (Library of Congress, IMLS, etc); other national governments (paid crawl services); foundation grants; universities and libraries (crawl, preservation, and digitization services); and of course general donations. The last category of course has the fewest strings and lets us pursue new projects which might be hard to get traditional funding for. Remember that the whole premise of web archiving was considered radical and quixotic at the beginning!

(source: I work at IA on scholar)