[Here’s what’s at stake in the meeting.]

What the world may learn when he meets with Mr. Kim for the second time in a year is whether he is willing to accept a weaker deal with North Korea — and whether he can sell it.

North Korea presents a far more difficult case than Iran. It already has an arsenal of as many as 30 nuclear weapons, as well as missiles that can reach the United States. Its devotion to that national project is so intense that Mr. Trump’s director of national intelligence, Dan Coats, angered him by saying last month that the North was “unlikely to completely give up its nuclear weapons and production capabilities” because they are “critical to regime survival.”

If Mr. Coats is right, the president’s warm embrace of Mr. Kim could encourage other countries to make a sprint for the nuclear finish line, convinced that in the end, the United States will learn to live with yet another nuclear power.

Mr. Trump hopes to be remembered in history for bringing peace to the Korean Peninsula. But he also risks becoming the president on whose watch North Korea demonstrated an ability both to hit the United States with a missile and to detonate a hydrogen bomb — and who then gave it such a good deal that others decided to build nuclear arsenals, too.

Even some hard-liners in Washington, though, see the potential of Mr. Trump’s gamble. “The stars have kind of lined up,” said Andy Kim, a former head of the C.I.A.’s Korea mission center, and the man who last year ran messages between the two leaders.

Speaking at Stanford University last week, he recalled that the young North Korean leader told Secretary of State Mike Pompeo in Pyongyang that he was thinking of the future: “I’m a father and a husband. And I have children. And I don’t want my children to carry the nuclear weapon on their back their whole life.”