Sentence:  Siberia, though it stands outside the territorial confines of Russia <WSD>proper</WSD>, constitutes an essentially component part .... Outer Mongolia, [so called] to distinguish it from Inner Mongolia, which lies nearer to China <WSD>proper</WSD>, revolted and declared its independence. 
Meaning of the word marked with <WSD> tags:  In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).