Midway through the press conference after his summit meeting with North Korean leader Kim Jong Un, President Donald Trump offered his basic argument for why this effort at diplomacy with Pyongyang will succeed where so many others have failed: “This is a much different time, and this is a much different president,” Mr. Trump said.

As that suggests, the prospects for turning Tuesday’s vague agreement into lasting change on the Korean Peninsula hinge on two new factors in the equation. The first is the calculation that Mr. Kim...