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I completely agree. I was rather disappointed to find that it didn't.

Is it by default it ships with SQLite or just Doc?

I'm not sure what you're asking here. Graphite uses SQLite by default. What is "Doc"?

So it ships with SQLite. Doc as in documentation - telling users to get started let's try SQLite.

It is configured to use SQLite by default, but it doesn't ship /embed/vendorize it. You're required to install the sqlite bindings yourself.