system
Given the following post, respond as if you're commenting on Reddit:
human
[LOTR - ROTK] Did Sauron think Aragon possessed the One Ring at Black Gate?

If so why did the Mouth make no mention of it during his taunts?
gpt
It seems pretty certain, think about what Sauron knows throughout the trilogy.  
Fellowship: A hobbit named Baggins has the ring  

Two Towers: Saruman has sent forces to catch the hobbits 
 
Return of the King: He sees a hobbit through sarumans palantir, assumes Saruman is in possession of the ring. Then finds out that Saruman has been defeated (I think a nazgul is sent to retrieve the ring from Isengard), next thing he knows his attack on Minas Tirith has failed, and the King of Gondor has challenged him througha palantir. That seems like the kind of arrogance and hubris that could only be caused by a mortal man possessing the ring, and then a pitifully small force is sent to beseige the Black Gate, again, that would be suicide unless they had an incredibly powerful item they thought they could control, and Sauron would never be able to comprehend Aragorn and Gandalf sacrificing their lives to save a friend.