Victor Cha is a professor at Georgetown University and senior adviser at the Center for Strategic and International Studies.

The footage of smiles, hugs and handshakes between the leaders of North and South Korea made for great television. But it also demonstrated that puzzling together peace on the ­Korean Peninsula still requires two missing pieces: Kim Jong Un’s true intentions regarding his nuclear weapons and President Trump’s ability to persuade the North Korean leader to part with his armaments. Thus, the Korea summit has only raised the stakes for the expected summit between Trump and Kim in May or June.

You can’t blame the Koreans for wanting to declare peace on the peninsula and finally put an end to the Korean War. The country did not ask to be divided in 1945 by the United States and the Soviet Union at the start of the Cold War. And despite the end of that war decades ago, the antagonistic relationship lives on, exacerbated by North Korea’s drive for nuclear weapons.

Peace declarations have been an integral part of the previous summits between the two Koreas in 2000 (Kim Dae-jung and Kim Jong Il) and in 2007 (Roh Moo-hyun and Kim Jong Il), as well as part of five joint documents dating to 1972. Still, there’s something different this time around. The language in the summit communique clearly reflects the urgency of South Korean concerns about the peninsula’s approach to the brink in 2017 with 20 North Korean ballistic missile tests, claims of a subterranean hydrogen bomb detonation, heightened U.S. military exercises and the U.S. president’s threats to rain “fire and fury” on North Korea. In this regard, North Korea’s reciprocal interest in diplomacy may reflect not just the persuasiveness of its southern counterpart’s diplomatic overtures but also concerns about Trump’s threats of war.

But what this summit highlights is the indispensability of the United States to a diplomatic solution for peace and an end to the nuclear crisis on the peninsula. The Koreans can declare peace, but a treaty that would end the 1953 Korean War armistice would require the United States (and China) as a signatory. And it is hard to imagine that Trump would sign such a piece of paper without the end of the nuclear weapons program in North Korea.

The summit unfortunately did not bring greater clarity to this piece of the puzzle. While the two Korean leaders confirmed the common goal of complete denuclearization and a nuclear-free Korean Peninsula, their statements fall far short of previous commitments by Pyongyang to abandon “all nuclear weapons and existing nuclear programs” in the 2005 denuclearization agreement I worked on as the the George W. Bush administration’s National Security Council representative. Nor do the statements come close to North Korea’s commitment in a previous inter-Korean agreement in 1992 to forswear the development and possession of nuclear weapons, as well as to prohibit reprocessing and enrichment facilities in their countries.

Perhaps Kim is saving this agenda item for his meetings with the United States. Or perhaps he never intends to give away his weapons and instead wants to have his cake and eat it, too — in the form of a peace treaty that would make it harder for the United States to carry out a preventive military attack, a photo op with the U.S. leader that legitimizes him as ruler of the newest nuclear weapons state, and the promise of lifting economic sanctions, all in return for a cap on nuclear weapons production and ban on missile testing.

South Korean President Moon Jae-in will come to Washington to meet face to face in the coming weeks with Trump and encourage him to go ahead with his planned summit with Kim to keep up the diplomatic momentum. And Trump, not one to shy away from the moment, will almost certainly oblige. But the stakes and the expectations have only been made higher by the Korea summit. Trump needs to respect South Korean desires for a peaceful diplomatic solution, but he should also maintain economic sanctions pressure on the North Korean regime, while at the same time compelling Kim to drop his weapons and embrace open-market forces that could have deleterious effects for his own autocratic rule.

Moreover, given the hype Trump has created around the meeting with his own tweets, he cannot break his own cardinal rule, which is never to want a deal more than your counterpart. This meeting will be a clear test of the president’s self-proclaimed negotiating skills, and the stakes could not be higher because failure would mean the end of diplomacy and a return to discussions of military options. After all, the only thing after a summit is a cliff.

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