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Unpaywall is based on Crossref DOIs (one-to-one records), and adds information about publicly accessible versions of each work. In theory publishers can register metadata about whether articles are OA or not with Crossref, but the quality and coverage of this metadata is poor in general.

Unpaywall will both check if articles are actually available from the publisher (by following the DOI and parsing the landing page), and by looking for other versions elsewhere on the web (eg, a pre-print). It is simple in theory, but doing this reliably for millions of DOIs from thousands of publishers is a lot of work!