On Monday the US National Security Adviser Robert O’Brien confirmed that the US was “keeping a close eye” on rumours suggesting that Kim Jong-un was gravely ill. These had begun following reports from North Korean defectors in South Korea that he had undergone heart surgery on 12 April, after which the North Korean leader had missed the “Day of the Sun” commemorations of his grandfather’s death on 15 April last week.

The rumours were played down by the South Korean authorities, who suggested that he was “touring provincial areas”, and by Donald Trump, who at his White House briefing yesterday called the rumours of Kim’s ill health “fake news”. Yet still several unanswered questions remain.

Question one: where is Kim Jong-un? The North Korean leader has now not been seen in public since, it is believed, 11 April. His absence at the unusually low-key 15 April commemorations was particularly striking as his grandfather, Kim Il-sung, was the country’s founder and revered as a near-deity there. With rumours swirling about his health - there have been reports of panic buying within North Korea - one might expect a healthy Kim to quash them by making an appearance.

Conversely, when Kim’s father, Kim Jong-il, died the news was covered up for two days as China brokered the succession. There have reportedly been signs of activity at a North Korean military facility used to train for parades. Also watch for any signs of changed flight activity between Beijing and Pyongyang.

Question two: does South Korea know something it is not sharing publicly? Chad O’Carroll, CEO of the Korea Risk Group, reports that Seoul last week briefed reporters on North Korean missile tests hours after the fact. Typically such tests are announced instantly. O’Carroll also finds it odd that the briefing included details of standard North Korean air activity, about which they only rarely talk. “Something seems to be up,” he concludes.

Question three: is the US government, contrary to Trump’s comment, in fact still taking the illness rumours seriously? Aircraft Spots, a Twitter account monitoring air traffic, on Wednesday tracked multiple US surveillance flights over North Korea. Such flights, reports Vice, are not uncommon but are not usually trackable - suggesting the US government may be trying to pressure the North Korean leadership into revealing what is happening by making them visible.

Question four: is China preparing for a humanitarian crisis? A well-placed source has said that China is buying up large quantities of rice and cooking oil through commodity-trading front companies, despite it having no obvious additional domestic requirements for these food supplies. This is, to stress, just one source and the claim has not been verified. But if correct it might suggest Beijing is preparing for a possible refugee crisis should the regime in Pyongyang collapse.

If Kim Jong-un is incapacitated or dies, such action would indeed be prudent. Kim Yo-jong, Kim’s sister and his close ally, would be the natural successor. But it is uncertain whether this patriarchal military dictatorship would accept a female leader. On the other hand, the North Korean system is built on near-religious veneration of the family of Kim Il-sung (on which, read this 2018 profile of the Kim dynasty by our commissioning editor Gavin Jacobson) which might dissolve should, say, an army general stage a coup. A potentially disastrous power struggle within this nuclear-armed state cannot be discounted.

To be clear: nothing about this is confirmed. And as O’Carroll notes, there have been no signs of regime commotion in Pyongyang or Dandong, the main border crossing between North Korea and China. Kim may be well, or ill but recovering. But he is overweight and known to live unhealthily. And something does indeed seem to be up. If North Korea’s leader is so ill that he can no longer control the regime, or if he dies or is already dead, the world will be presented with another enormously destabilising event at the very moment when it can least afford it.