Although Trump has spoken warmly of Kim since meeting him last year, the agreement signed by the two leaders was notably light on details. At 400 words, it was far more brief than most international agreements. And though it set out four areas of agreement between the two sides, it framed those areas so vaguely that analysts wondered whether Washington and Pyongyang had the same interpretation of the document they signed.

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Here are those four areas — and what has happened on each subject since the Singapore summit.

“The United States and the DPRK commit to establish new U.S.-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity.”

“Peace and prosperity” are certainly lofty goals, but it’s not clear what working toward them means in practice.

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After the Singapore summit, attempts to establish U.S.-North Korea working groups ran into difficulties. Secretary of State Mike Pompeo struggled to make progress in his meetings with North Korean counterparts, while Stephen E. Biegun, the U.S. special envoy to North Korea, initially struggled to get meetings with North Korean officials at all.

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There have been some signs of progress here in recent months. Notably, Biegun has been able to meet his North Korean counterparts since the second summit was announced. The two sides have also discussed opening liaison offices in each other’s countries — a possible step toward formal diplomatic relations.

But U.S.-led bilateral and multilateral sanctions on North Korea remain in place, much to the chagrin of Pyongyang. The U.S. government is still demanding progress on denuclearization before those sanctions can be lifted.

“The United States and the DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula.”

This vague statement overlapped a lot with the first, but the mention of a “peace regime” was important.

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A peace regime means a formal end to the Korean War. That conflict ended in 1953 with an armistice, but an official peace was never reached. The peninsula technically remains at war, and the demilitarized zone between the two Koreas is still one of the most tense borders in the world.

While North Korea has long wanted a formal end to the war, previous U.S. administrations have argued that such negotiations could happen only after Pyongyang gave up its nuclear weapons. But there is widespread speculation that Trump may announce that he intends to end the war or even agree to a peace treaty.

Either of those options would be complicated. The other parties to the war, including China, would need to be involved. A peace treaty could also require the consent of Congress, which might balk at a measure that could undermine the argument for keeping U.S. troops in South Korea.

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In the meantime, there have been positive steps. Increased inter-Korean cooperation has led to a more peaceful atmosphere on the peninsula, and South Korea has removed some military positions near the DMZ. The United States and South Korea have also suspended a number of joint exercises in what the Pentagon’s chief spokeswoman has described as a move “to give the diplomatic process every opportunity to continue.”

“Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work toward complete denuclearization of the Korean Peninsula.”

When Kim first met his South Korean counterpart, President Moon Jae-in, in April, the two leaders signed a declaration that they would work toward “a nuclear-free Korean Peninsula.” Trump and Kim reiterated this aim at their Singapore summit.

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But the meaning of “complete denuclearization” isn’t necessarily obvious. The United States views it as the “complete, verifiable and irreversible” end of North Korea’s nuclear program. But North Korea may have a broader definition that includes the removal of nuclear-armed U.S. bombers and submarines from the area — or even the removal of all U.S. troops from South Korea.

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There has been progress on North Korean nuclear weapons recently. Pyongyang hasn’t tested a nuclear weapon since September 2017, and its last missile test came a month later. It also destroyed Punggye-ri, a nuclear testing site, in May. But those were unilateral moves that took place before Trump and Kim met. There has been little action since then. And while North Korea isn’t overtly testing weapons, it may still be producing them.

“The United States and the DPRK commit to recovering POW/MIA remains, including the immediate repatriation of those already identified.”

The agreement to let the United States recover the remains of U.S. troops from the Korean War was the least ambiguous of the Singapore aims — and perhaps the most successful. Fifty-five sets of remains were returned in a ceremony in July.

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But the United States would like to obtain more remains from North Korea and to have American researchers be allowed into the country to search for remains, as they were in the past.

In a statement released last week, the Coalition of Families of Korean and Cold War POW/MIAs — an organization that brings together families of U.S. troops lost in foreign wars — said that negotiations to resume joint operations had “stalled” and that “remains of U.S. servicemen already exhumed in the DPRK wait to be returned.”