The rush to applaud today’s news of a political breakthrough in Ukraine is understandable after the truly horrible, unforeseeable events of the past week. Everyone in Western European capitals and Washington clearly is invested in this deal succeeding. Western officials want an immediate halt to the dramatic spiral into violence, repression, and separatism that carried a clear risk of a Yugoslav-style meltdown in a country of 45 million.

It’s also remarkable that top diplomats like Frank-Walter Steinmeier of Germany and Laurent Fabius of France were willing to put their governments’ credibility on the line after several months of EU dithering and fecklessness in the aftermath of the disastrous Vilnius Summit.

Yet now comes the hard part.

The terms of the deal contain several provisions that may prove exceedingly difficult to implement. The most obvious is the demand that all “illegal weapons should be handed over to the Ministry of Interior bodies within 24 hours” and that all parties should respect laws governing the illegal carrying and storage of weapons. Unfortunately, televised images of yesterday’s deadly firefights in Kyiv leave no doubt that there are plenty of weapons on both sides.

The trio of opposition leaders who signed today’s agreement clearly do not control radical and paramilitary groups who have taken the lead in organizing popular armed resistance to President Yanukovych’s forces nor necessarily a majority of the people who have defended Maidan. One of these groups, Praviy Sektor (Right Sector) has already come out against today’s agreement, denouncing it as “eye-washing” and vowing to continue the national revolution.

The ugly fact remains that we still do not know for certain what kind of role such groups or Yanukovych loyalists played in touching off this past week’s violence. Until that part of the picture becomes clear, all eyes must be on the people with the guns, not the politicians.