Donald Trump and Kim Jong-un have taken us on a roller-coaster ride of nuclear hopes and disappointments, from the high of their historic summit in Singapore last June to the low of their second summit that departed from script and collapsed in disarray in Hanoi . The world is left clinging to the bottom line that North Korea will maintain its pause in the testing of nuclear weapons or long-range missiles. The US president says he believes the North Korean leader will stick to that promise: “I trust him and I take him at his word. I hope that is true.” Beyond that there is not even a plan for a third summit at this stage. But so long as Kim avoids nuclear provocations there has to be hope that continued negotiations through backchannels, free of the pressures of global and domestic expectations of a major summit, get around obstacles so intractable they prompted the two sides to abruptly cancel lunch and a joint signing ceremony yesterday and head home empty-handed. The sticking points were apparently reciprocal. Trump said he was unwilling to lift sanctions in return for North Korea dismantling its Yongbyon nuclear facility. Kim wanted sanctions lifted first. A formal end to the state of war between the two sides thus remains a distant goal. The outcome also reflects Kim’s new year speech, when he said that if the US continued with sanctions, North Korea “might” be obliged to seek a “new way”. Redoubled negotiating efforts with redoubled patience on both sides would be a safer option for the world than the harder line signalled by this language. Having helped facilitate the summit, Beijing has an interest in seeing the process is not entirely wasted or momentum allowed to lapse. Though it was a letdown for the nuclear disarmament cause, the collapse of the summit did not entirely come as a surprise. Trump had been lowering expectations as the second summit approached. As this newspaper noted on the eve of the Hanoi meeting , where once he was talking about a quick deal for Pyongyang to dismantle its nuclear programme, the message had changed to there being no rush as long as a halt to the testing continued. That is more realistic, and more likely in the end to yield genuine, lasting improvement to prospects of peace and security on the Korean peninsula. After all, the lifting of sanctions and the full dismantling of Pyongyang’s nuclear programme is likely to be an incremental process of trust-building. Now that North Korea is a nuclear power, continued talks will help ensure that Kim is less likely to feel the need to use it. In that regard it is good to hear Trump say the relationship with Kim remains strong, and that US Secretary of State Mike Pompeo expressed optimism and “hope that we’ll [get a bit further] in the weeks ahead”.