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"context object" is defined as "the object on which the method or attribute being discussed was called". "active range" is defined as "The active range is the first range in the Selection given by calling getSelection() on the context object". However, in the context of the definition of "active range", there isn't a method or attribute being discussed, so the term "context object" is undefined. If we assume that the definition of "context object" is to be inherited from wherever the term "active range" is defined, then this fails in the case of the "Additional Requirements" section, where user interaction results in calling algorithms that rely on the active range, despite no method or attribute being involved at all at any point.
Yeah, I've been really lazy with the use of "context object". Really I always mean "current document", loosely speaking, but I have to be more precise here.