The agreement’s value lies in opening the door to an Afghan peace process — it will retain its salience only if it is followed by that next phase. So the details may not matter all that much.

Some have criticized the possible U.S.-Taliban agreement as nothing more than a fig leaf for American military withdrawal. But if all the United States wanted to do was leave Afghanistan, it could do so without making a deal with the Taliban. And if intra-Afghan negotiations fall apart, it is hard to imagine the United States will feel bound by whatever it has agreed with the Taliban. Ultimately, America will pull out of Afghanistan on its own terms — just as it invaded and dialed up and down its troop numbers in accord with American interests.

On the flip side, the Taliban will only have reason to abide by its antiterrorism promises if a peace agreement helps it become part of the political mainstream and gain a stake in maintaining the legitimacy it has already begun to enjoy.

Making the most of this opportunity will not be simple: The next stage of talks could easily consume a year or more. They will have to tackle much thornier questions of how to share power and security responsibilities and how to modify state structures to satisfy both the government’s interest in maintaining the current system and the Taliban’s interest in something they would regard as more Islamic.

What’s more, there are no doubt some on both sides who maintain maximalist aspirations, still hoping to exclude the other side from power by any means. These elements will be inclined either to provoke failure of the talks or to outlast American and other outsiders’ pressure to persevere.

The most important task now is to start and generate traction in intra-Afghan negotiations, without getting distracted by those who might seek to capitalize on the fragility of the “reduction in violence” pledge or any cease-fire agreements that follow. It is nearly certain there will be continued violence during the talks.

Patience is an absolute necessity. A peace process won’t be done as fast as long-suffering Afghans hope, nor quickly enough to produce a definitive political win before the American presidential election. And a durable peace process needs a neutral mediator to manage it, help to bridge mistrust and nudge the parties toward compromises. This can’t be the United States, which isn’t neutral in the Afghan war. But there won’t be a neutral mediator without American backing for the idea.