I have an idea for an alternative world-map projection. Is there a (simple) public data-source which indicates for each longitude/latitude-location whether it is land or sea I could use for this purpose? As an added bonus longitude/latitude of state-borders would be nice.

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My favorite one is OSM: https://wiki.openstreetmap.org/wiki/Downloading_data. But it can be an overkill for your task. NaturalEarth has a few datasets: https://github.com/nvkelso/natural-earth-vector (https://www.naturalearthdata.com/downloads/)

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