It's August 2nd of 1945. What facts in place at the time (and I'll give a wide degree of latitude here to include anything from a well-documented historical record as a "fact") made it absolutely imperative for the U.S. to drop atomic bombs on Japanese cities at that point in time?
An analysis based on the presumption that "I must do X to you because the only alternative I have is to accept Y" is a poor line of thought here in a military conflict at that particular juncture.
What is the alternative to X and Y that I am obviously missing? It seems to me that X was dropping the bombs, which we did, and Y would have been a conventional invasion of Japan. What was Z; what was the other alternative to bring the war to a conclusion?