But in many recent cases, it seems that the Islamic State's media apparatus is also waiting for those revelations. Since the highly coordinated attacks in Paris last November, most of the attacks that the group eventually claimed were carried out by individuals who may never have come into direct contact with operatives in their supposed "caliphate" in northern Iraq and Syria. These attackers did not give the Islamic State notice that they would be acting in its name. Instead, some of them self-radicalized and left behind recordings offering oaths of allegiance.

By reading the language in the Islamic State's claims on attacks, one can see which of them were heavily directed, as in Paris and Brussels, and which were simply inspired by the group's ideology. There is a clear difference between claims made after attacks that Islamic State leaders knew about beforehand, and attacks they didn't know about.

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In the case of Paris, for instance, highly detailed news releases were distributed right after the carnage, complete with videos and pictures. On the other hand, Amaq, the Islamic State's media arm, claims responsibility for "inspired" attacks only once it gets credible information of a link, either from a source of its own or from the news media. The Islamic State, also known as ISIS, does not always have its own inside source.

"What has evolved is that they are doing much the same thing that we do as analysts, which is watch these attacks and try and figure out if it is ISIS-inspired," said J.M. Berger, a fellow with George Washington University's Program on Extremism and the co-author of "ISIS: The State of Terror."

After a man blew himself up in Ansbach, Germany, on Sunday, it took Amaq 19 hours to claim that the Islamic State inspired the attack. After a 17-year-old ax-wielding Afghan went on a rampage on a train, also in Germany, it took nine hours to issue such a claim. After Mohamed Lahouaiej Bouhlel mowed down dozens in Nice with a truck, it took a full day and a half.

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“For these inspired attacks, it's important to know that [the media people in Syria] don’t even know of these guys. They have nothing to do with them. They aren’t in contact with them directly," said Amarnath Amarasingam, a fellow studying extremism at Dalhousie University in Canada and the co-director of a study of Western fighters for the Islamic State, based at the University of Waterloo in Ontario, Canada.

The lag time in claiming an attack reflects a need to establish a credible link between the attacker and the Islamic State. Many have lampooned the Islamic State as an organization keen to claim each and every terrorist attack around the world, but analysts say it has a vested interest in being accurate.

"They’re careful about it. They couch their terms a bit," said Berger. "If they can credibly insert themselves into the narrative around an attack, they win, essentially."

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In other cases, though, it has proved effective for ISIS to claim attacks in which the link is far sketchier. For instance, in the San Bernardino, Calif., attack last December, the media widely reported that the couple who carried out the attack had posted an oath of allegiance to ISIS on Facebook. Amaq then proclaimed them "soldiers of the caliphate." But the FBI never confirmed that the Facebook post was ever written, and Director James B. Comey said at the time, "I’ve seen some reporting on that, and that’s a garble." San Bernardino nonetheless gave ISIS the chance to claim its first "inspired" attack on American soil.

Beyond credibility issues, the hesitance to immediately claim the attacks such as the most recent ones in Germany and France may also reflect embarrassment the group felt after associating with particular lone-wolf attackers. In the weeks following their attacks, news reports indicated that Bouhlel, the attacker in Nice, and Omar Mateen, who killed 49 people at an Orlando nightclub in June, may have had sexual relationships with other men. Mateen and Bouhlel were each embraced by ISIS before that became public, and homosexuality is punished through gruesome death penalties in the "caliphate."

In cases like those, attackers unvetted by the Islamic State may still be at worst a double-edged sword for the organization. After all, despite bad publicity, ISIS can still claim that it inspired those attacks. And the greater the perceived threat from the group becomes, the more it may stir calls for larger-scale retaliation or anti-Muslim policies, leading to the radicalization of others.

Tuesday's killing of an octogenarian priest in France yielded a relatively quick claim. Between "directed" and "inspired" attacks, it seems that this one lies somewhere in the middle of the spectrum. News reports quickly uncovered one of the attackers' attempts last year to travel to Syria. Amaq's statement, pictured above, called the men "executors" and "soldiers of the Islamic State," but more or less acknowledged that ISIS had not directed the attack. Instead, as in other "inspired" attacks, Amaq said the men had responded to a call for attacks to be carried out in countries participating in the coalition fighting ISIS in Iraq and Syria.

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But it attributed its claim to an "insider source," whom Amarasingam said was likely to be someone the attacker was in touch with during his failed "hijra," or migration, to Syria last year. The seemingly part-directed, part-inspired nature of the attack poses a dilemma for law enforcement in the West: Does preventing people from traveling to Syria increase the likelihood of an attack at home?

"That’s been part of ISIS's propaganda," said Amarasingam. "You either pack your bags or sharpen your knives. And if you’re unable to travel here and join the caliphate, either because you can't afford it or law enforcement is watching you, you do have another recourse, which is to defend us wherever you are."