The Rudy 2013 mayoral campaign lasted slightly less than 24 hours — from the time the trial balloon was floated in yesterday’s delightful Cindy Adams Post column to when it was definitively popped by a Giuliani spokeswoman last evening. The idea was immediately risible — an associate of the former mayor laughed, hard, when I called for a comment — but its possible roots are still interesting. Today’s Post, citing “insiders,” guessed that Judith Nathan was the one pushing Rudy to run. Maybe, but Adams and her paper have in the past been a vehicle for the mayor’s race musings of Ken Langone, the Home Depot co-founder, and Dick Grasso, the former New York Stock Exchange head, and especially their attempts to draft Ray Kelly. “They’re trying to stay relevant, and they don’t like the Democratic field,” a political strategist says. Adams was correct, however, that the city charter allows anyone who has served two full terms in City Hall to run again, after a break of at least four years. Stay tuned for the Ed Koch rumors.