But it is worth considering for a moment the somewhat different story Kim Jong Un is no doubt telling his own domestic audience – as well as a receptive international audience.
"My determination to develop a nuclear capability has paid off big-time," he will say.
"The leader of the most powerful country in the world has asked to meet me and seek a deal. As the leader of a nuclear-armed state, I meet him as an equal. And he needs me more than I need him; he has to convince his people that the meeting was a success, so he will have to rely on me to deliver what he wants. That leaves him as the supplicant and me with the power."
And Kim can go further.
"Having established this elevated status for my country," he can say, "I have been able to show how magnanimous and far-sighted I am. Now that we have nuclear-armed missiles that can reach America, I do not need further nuclear tests and rocket trials, so I will happily offer a 'concession' to conduct no more tests; I already have all the capability I need to make sure that no one pushes us, or me, around.
"I am happy to give assurances not only to the Americans, but also to the Japanese, and others nervous about our ability to attack them, that we have no intention of doing so. And I have been able to underline our peaceful intentions by making new overtures to our brothers in South Korea, bringing an end to the state of war between us, showing Koreans in both the North and the South that we are one people and that I am the one person with the strength and vision to unite them. No one should be surprised that both our allies in China and my own people welcome the initiatives I have taken."
It isn't a bad story, is it? It provides a persuasive alternative to the American account of what has happened and is happening. Like the Trumpian story, it is of course designed to identify the teller as the hero, and to place him centre-stage; but, tellingly, and unlike the Trump story, it has the additional virtue of corresponding quite closely with the facts and – for that reason – it is more likely to be believed around the world.
The American President will continue, no doubt, to try to convince his voters that he deserves the credit for bringing about a rapprochement between the two countries, but the fragility of that claim can be seen from the fact that he (through his national security adviser, John Bolton) felt the need to threaten the North Korean leader that, if he did not come up with a complete acceptance of American demands in Singapore, he could suffer a "Libyan" outcome – an allusion to the fate, (one of deposition and eventually murder), suffered by the Libyan dictator, Colonel Gaddafi.
Trump, having plunged the Middle East into turmoil with his decisions to pull out of the non-nuclear deal with Iran and to relocate the American embassy to Jerusalem, needs a success in Singapore, but – as things stand – Kim, displeased by the Libyan allusion, and by US military manoeuvres in South Korea, may not even bother to turn up.
It seems obvious who holds the trump cards.
