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How does this compare to https://languagetool.org, which is also open source?

I'm not sure what kind of AI Languagetool uses but it works really well!

LanguageTool is not open source; it is open core. There are proprietary "premium rules," and you won't get them in a self-hosted version.

Self hosted & open core seems distinctly better than an open wrapper around a black box core that's hosted by a 3rd party.

They use the LGPL license for a lot of their work.