North Korean leader Kim Jong Un began the talks on Thursday morning claiming he was willing to denuclearize, but by Thursday afternoon President Trump was forced to admit that after a year of engagement with Kim, two summits with the United States and three with South Korea, there was still no agreement on what denuclearization means.

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“He has a certain vision,” Trump said. “It’s not exactly our vision, but it’s a lot closer than it was a year ago.”

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On Thursday afternoon, South Korean President Moon Jae-in was on the phone to Trump offering his services as mediator and even suggesting they meet in person in the near future for more “in-depth” discussions.

Trump said he had no plans to meet Kim again for a third summit. But on Friday, Secretary of State Mike Pompeo said the United States was “anxious to get back to the table so we can continue the conversation that will ultimately [lead] to peace and security, a better life for the North Korean people and a lower threat.”

China, a neighbor keenly interested in the success of the talks, hoped there would still be a way to find a compromise.

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“As an old Chinese saying goes, the road to happiness is strewn with setbacks. However, I believe that a bright future awaits,” said Foreign Minister Wang Yi.

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North Korea, meanwhile, called the summit “successful” — although nothing that Kim ever does could really be described any other way — and the state news agency said the two men had agreed to “keep in close touch with each other for the denuclearization of the Korean Peninsula.”

But a more revealing insight into the minds of the North Korean negotiators came at an extraordinary news conference held by the country’s foreign minister and deputy foreign minister after midnight in Hanoi.

“The impression I got observing this summit from the side was that our chairman seems to have difficulty understanding the U.S. way of reckoning,” Vice Foreign Minister Choe Son Hui told reporters. “I felt that our chairman has lost the will to engage in dealmaking, with the United States saying that even a partial lifting of sanctions for the civilian economy is hard.”

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Different versions of the breakdown were presented by both sides, but the fundamentals of what North Korea was prepared to agree to were beginning to emerge a day after the failed summit.

Foreign Minister Ri Yong Ho said North Korea had offered to close down the Yongbyon Nuclear Research Center, a large complex that covers more than three square miles and includes about 300 buildings.

Yongbyon is the site of North Korea’s main, aging nuclear reactor, which has been the regime’s only source of plutonium, although satellite imagery suggests that the reactor was largely not operating last year, possibly because of maintenance work.

It is also home to a new light water reactor that has never been inspected as it is not thought to be operational yet, experts say. Choe said North Korea offered to close a facility to enrich uranium that was shown in 2010 to nuclear scientist Siegfried Hecker.

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“They were pretty expansive with respect to what they were prepared to do at Yongbyon, but there was still not complete clarity with respect to the full scope of what they were prepared to offer,” Pompeo said Friday in Manila.

A senior State Department official said it was important to be precise about what exactly is being done at Yongbyon, but “the North Koreans struggled to give us a precise definition.” He characterized the North Korean offer as the closure of a “portion” of Yongbyon.

Experts and intelligence officials say they believe North Korea has other covert sites to enrich uranium in other parts of the country. Closing Yongbyon entirely would slow North Korea’s ability to produce fissile material for bombs but not stop it entirely. To achieve that goal would require a complete declaration of all fissile material sites in the country, and the ability to conduct extensive and intrusive inspections at short notice. That is not something North Korea has ever agreed to.

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Closing Yongbyon would also leave North Korea’s arsenal of nuclear weapons and missiles intact.

In return, Trump said North Korea had basically asked for sanctions to be fully lifted. Ri, the foreign minister, took issue with that characterization, arguing that Pyongyang wanted only a “partial” lifting of sanctions and citing the most recent five out of 11 sanctions packages imposed by the United Nations Security Council.

But the senior State Department official said the sanctions request included “metals, raw materials, transportation, seafood, coal exports, refined petroleum imports, raw petroleum imports.” The official, who spoke on the condition of anonymity under State Department guidelines for the briefing, added: “It was basically all the sanctions except armaments.”

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Benjamin Katzeff Silberstein, an economics and sanctions expert at the Stimson Center, agreed that Ri had basically demanded the lifting of all “meaningful” sanctions. “What Trump said was basically the truth, in other words,” he tweeted.

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In effect, the United States was being asked to give up almost all of its leverage in return for an offer that would not prevent North Korea from making new bombs and missiles and would leave its current arsenal untouched. It would have given Kim the economic rewards he sought and left North Korea as a de facto nuclear weapons state.

“The dilemma that we were confronted with is the North Koreans at this point are unwilling to impose a complete freeze on their weapons of mass destruction programs,” the State Department official said. “So to give many, many billions of dollars in sanctions relief would in effect put us in a position of subsidizing the ongoing development of weapons of mass destruction in North Korea.”

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At the Center for a New American Security, Duyeon Kim said she was encouraged by signs that both sides wanted to keep diplomacy alive. But she said it was clear they have a lot of work to do.

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“No deal is certainly far better than a bad deal, but a missed opportunity was not setting a date, even a rough one, on when their negotiators would meet again,” she said. “The longer there is no real nuclear deal, the more time Pyongyang has to produce more nuclear weapons.”

Ri, meanwhile, said it was “difficult to say” if there would be a better offer than the one presented in Hanoi.

“Our principal stance will remain invariable and our proposal will never be changed, even though the U.S. proposes negotiation again in the future,” he said.

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Joseph Yun served as the U.S. special representative for North Korea from October 2016, under the Obama administration, to March 2018, under Trump. He says the negotiations may have hit a fundamental roadblock.

“Trump is beginning to realize that North Korea’s not going to completely denuclearize, not now and probably not ever. I think he will have a tough time over that realization,” he said. “Both men have lost face.” That may make it even harder for working-level negotiators to get traction.

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Many experts say North Korea views nuclear weapons as essential to the survival of the regime, which is Kim’s only real priority. Given the fate of Moammar Gaddafi in Libya and Saddam Hussein in Iraq, that is perhaps understandable — even if it condemns the people of North Korea to live under a regime of totalitarian oppression.

Daniel Sneider, an East Asia specialist at Stanford University, said previous agreements with Pyongyang in the past three decades have always fallen apart when North Korea is asked to come clean about its nuclear industry and start to properly dismantle it.

“When you get to the point that North Korea has to do things to prove it is committed to full denuclearization — boom, they collapse,” he said.