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If the collective mass of everything else (the author excludes objects with vastly different orbital periods, but this is insignificant for the Solar System) that is in orbit around the Sun and passes through the orbital zone is less than 1% of the mass of the candidate object (and the object is too small to be a star, what the paper calls a "substar"), then it is considered a planet in this paper.
The term "brown dwarf" was originally coined by Jill Tarter in 1975 to describe these objects, and there were other suggestions for names, like planetar and substar.