In an indication of the breathless nature of the online rumor mill, one story circulated on social media in China went so far as to name the engineer of the purported coup, Vice Marshal Jo Myong-rok. The only catch: Mr. Jo was reported to have died several years ago.

One reason for the proliferation of theories is that rumors in North Korea have sometimes turned out to be true. These include news of the country’s devastating famine in the 1990s as well as the more recent (and unpopular) currency reform, which in both cases first surfaced in poorly sourced reports.

But there is also always the temptation to believe the worst of a family-ruled country that has little exposure to the outside world and has displayed its share of oddities, and cruelties. At least in earshot of their many minders, regular North Koreans credit the Kims with godlike feats. And although experts say Mr. Kim did not feed his uncle to dogs as one Chinese blog post suggested, South Korean intelligence officials said some of the uncle’s lieutenants were executed by machine gun.

In gauging what has happened to Mr. Kim, some analysts have noted that his father and grandfather also disappeared for weeks on end.

“Kim Jong-un’s disappearing act over the past month, in the North Korean context, is not an aberration,” said Lee Sung-yoon, a North Korea expert at Tufts University’s Fletcher School of Law and Diplomacy. “Such vanishing acts would be most unusual in democracies, but in totalitarian North Korea, Kim is the state. He is free to come and go as he pleases.”

Mr. Kim, however, has never been gone from sight this long and, until now, had been notably visible, visiting farms, factories and military units more frequently than his reclusive father did.

The visits are always covered prominently in the North’s state-controlled news media and include what passes for statecraft in North Korea; like his father and grandfather, Mr. Kim is followed on the “on-site guidance tours” by party functionaries and generals about twice his age who furiously scribble down his thoughts on how to make improvements.