While some in Washington’s national security community believe North Korean leader Kim Jong-un has been pushed aside by a secret coup, the leading theory among intelligence officials is that the young dictator has disappeared from public view because he is bedridden with a bad case of gout brought on by heavy smoking and too much caviar.

Either way, speculation about a power shift in the world’s most opaque regime is focusing on whether Mr. Kim — who hasn’t been seen in public in more than a month — will reappear Friday for a massive rally in Pyongyang celebrating the founding of the ruling Worker’s Party once headed by his father and grandfather.

U.S. intelligence sources this week dismissed claims by some regional analysts, as well as one prominent former North Korean counterintelligence official living in South Korea, that Mr. Kim has been deposed by a group of officials once loyal to his father, Kim Jong-il.

“The fact that Kim Jong-un is out of sight is not necessarily an indication that he’s not in control of the country,” a U.S. intelligence official told The Washington Times. “Despite the rumors, there are many indications that the country is functioning as it normally does.”

Other sources who spoke with The Times said a leading theory among U.S. officials is that Mr. Kim, who was last seen limping badly, is suffering from an intense case of gout — a form of arthritis that causes pain in the big toe and can be brought on by eating too much rich food.

North Korean officials have denied that Mr. Kim’s public absence is health-related, and Pyongyang’s state-controlled media have reported almost nothing about his disappearance.

But South Korean officials have suggested they have intelligence confirming that the 31-year-old dictator is suffering from some sort of ailment.

South Korean Defense Minister Han Min-koo said Mr. Kim is believed to be staying in the countryside north of Pyongyang as he recovers from an undisclosed illness, Seoul’s Chosun Ilbo newspaper reported Wednesday.

The South Korean and U.S. claims run counter to speculation brewing since last month, when a group of high-level exiles from North Korea gathered for a conference in the Netherlands to discuss the state of the regime they once served.

During a keynote address at the conference, Jang Jin-sung, who served as a counterintelligence official and poet laureate under Kim Jong-il before defecting to South Korea in 2004, asserted that North Korea is in the throes of a secret political civil war, according to an Oct. 2 report by Vice News.

The report said Mr. Jang told the conference that members of North Korea’s Organization and Guidance Department — a powerful group that once reported only to Kim Jong-il — have stopped taking orders from Kim Jong-un and effectively have taken control of the government in Pyongyang.

Some regional analysts have pointed to Mr. Jang’s remarks as evidence that Mr. Kim has been pushed to the sidelines.

“I think he has been or will soon be reduced to a figurehead,” independent analyst Gordon Chang told The Times this week.

But there is good reason to believe Mr. Kim is alive, Mr. Chang said.

“The regime derives its legitimacy from the Kim bloodline,” he said. “If Kim were formally disposed, the regime would have to find another basis of legitimacy.”

With such factors as a backdrop, Mr. Chang believes the real power in North Korea may have “diffused to a group of stakeholders that include Gen. Hwang Pyong-so.”

The theory is rooted in speculation that a cadre of officials has been engaging in secret maneuvering in Pyongyang over the past year. Such maneuvering, Mr. Chang said, would have begun in the wake of a December show of power by Mr. Kim, who was reported at the time to have ordered the execution of his uncle and close adviser, Jang Song-thaek.

U.S. officials, speaking anonymously, have said the execution was likely an attempt by the young leader to shore up his authority over much older government officials in Pyongyang.

But Mr. Chang said it likely triggered wider unrest around Mr. Kim.

“Jong Song-thaek had one of the most sophisticated patronage networks in the regime,” he said. “When you attempt to eradicate a patronage network like that, there’s going to be all sorts of turbulence.

“It’s logical to think that the remnants of the patronage network are going to seek revenge. I’m not saying this regime acts in a logical manner, but you’ve got to come up with evidence that says the logic doesn’t work.”

Mr. Chang pointed to the ascent of Gen. Hwang Pyong-so. During the years since the 2011 death of Mr. Kim’s father, Kim Jong-il, Gen. Hwang has risen quietly to become vice chairman of the National Defense Commission.

Gen. Hwang made international headlines Oct. 4 by leading a surprise delegation from North Korea to South Korea to attend the closing ceremony of the Asian Games.

With uncertainty about Mr. Kim’s disappearance from public, the visit triggered speculation that Gen. Hwang may be trying to inject himself into the heart of long-stalled peace talks between the North and South.

However, some respected North Korea analysts have downplayed the visit as anything unusual and suggested that Gen. Hwang’s move is likely unrelated to Mr. Kim’s absence.

A posting on the website of 38 North, the North Korea monitoring project at Johns Hopkins University’s School of Advanced International Studies, said Gen. Hwang and three other North Koreans “had lunch with South Korean Unification Minister Ryoo Kihl-jae and Defense Minister Kim Kwan-jin” during the visit.

The posting referred to a Chosun Ilbo report claiming the North Koreans told their hosts that Mr. Kim’s health was not an issue and extended “warm greetings” from Mr. Kim to South Korean President Park Geun-hye.

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