The North Korean summit is over. Now for the hard part.

The work ahead will be hard and perhaps impossible. Pompeo's first task will be to demonstrate that there indeed is a shared understanding of what the two sides mean by "complete denuclearization," and to elicit a weapons declaration and lock in a timetable for their destruction. The administration should test the possibility that Kim is sincere about disarming without giving away tangible benefits ahead of true demonstrations of commitment. On that count, Trump's pledge to suspend joint military exercises with South Korea was a step in the wrong direction.

Throughout the process, the administration should recall that in Kim it is dealing with a true tyrant: a leader whose government virtually enslaves its population and keeps them in ignorance and poverty. Its terrible human rights record has no parallel in the world today. Presidents have met with — and legitimated — other brutal dictators when the benefits (Stalin fighting Hitler, for example, or Mao balancing the Soviets) were likely to outweigh the obvious costs. The key is to get something important in return.

The bottom line: Until Pyongyang starts destroying its nuclear weapons, the United States will not have gotten that something. And so the difficult phase now begins.

Richard Fontaine is the president of the Center for a New American Security.