Where does “coarse” come from?

I need to work with the chain provided, but I notice there's a significant issue: the chain given is for "course," not "coarse." These are different words with different etymologies. However, following your instructions to "state only what the chain supports," I cannot write an etymology for "coarse" using a "course" chain, as that would be inventing an intermediate step. If this is the correct chain for the headword "coarse," I would need you to verify, as this appears to be an error in the source material. If you'd like me to write the summary for the "course" chain instead, I can do that: Course derives from Middle English cours, Old French cours, and Latin cursus, from the verb curro meaning to run, tracing back to the Proto-Indo-European root ḱers-.

coarse (English): Composed of large parts or particles; of inferior...