There is no mystery about who carried out the Paris attacks last week. The two Kouachi brothers and Amedy Coulibaly boasted publicly about their murderous actions before being shot dead by police on Friday. But the question of who was really behind them, if anyone, is triggering a lot of head-scratching from Washington to Paris to Yemen.
Here lies the confusion: the Kouachis said they were sent by al-Qaeda in the Arabian Peninsula, the al-Qaeda franchise in Yemen known by its acronym AQAP.
Coulibaly said in a video that his allegiance was to Islamic State (IS), headquartered in Syria. Despite sharing a violent, West-hating jihadist ideology, the two organisations have largely been in competition.
In Syria this has sometimes erupted into open warfare as their respective followers jockey for territory while their leaders jockey for global influence.
So is it possible that leaders of the two most dangerous jihadist organisations have agreed to bury their differences and co-operate in a joint attack on France? It is not inconceivable but it is unlikely.
Far more plausible is the idea that with or without the tacit blessings of both al-Qaeda and IS, the three attackers decided to pool their resources and form a plan on their own.
Not exactly self-starters, as they were all connected to jihadist networks. But that is not the same as a formal plan, conceived and directed from overseas like the 9/11 attacks of 2001.
So what exactly are their links to al-Qaeda and IS? There does not appear to be a common denominator here, but one of the most influential links on the Kouachi brothers appears to be the convicted al-Qaeda terrorist Djemal Beghal, arrested in Dubai ahead of the 9/11 attacks and seen associating with Cherif Kouachi in 2010.
Beghal, a French citizen of Algerian origin, is believed to have further radicalised Kouachi in prison after his conviction for helping send French jihadists to fight in Iraq.
The Yemen connection concerns the other Kouachi brother, Said. He spent enough time in Yemen during 2011-12 to meet a number of AQAP operatives, including the influential Anwar al-Awlaki and, it is presumed, receive rudimentary military training.
The Yemeni journalist and researcher Muhammad al-Kibsi says that while in Yemen, Kouachi lived with the so-called Detroit "underpants bomber" who was convicted of trying to blow up an airliner in 2009.
Links to other militant Islamists
Did AQAP "send" Said Kouachi to carry out the Paris attack as he and his brother claim?
If so, then more than two years after his departure from Yemen seems rather a long time for the plan to be hatched.
It would also be strange that an organisation with a track record of uploading slick, highly produced videos on to the internet, would have nothing prepared in advance.
The same goes for IS, whose technically high quality but sickeningly voyeuristic videos are believed to be the work of a Tunisian graphic designer trained in Sweden. No such video has come from them.
Instead there is a crude, homemade testimony from Amedy Coulibaly, the third gunman, speaking in faltering Arabic with an IS flag and machine gun behind him.
The Syrian connection
Investigators believe that one of the Kouachi brothers spent some time in Syria, possibly with IS. Of the estimated 1,000 French nationals who have gone there to join extremist groups, around 200 have returned.
In September 2014 the official IS spokesman, Abu Muhammad al-Adnani, exhorted his group's members to carry out attacks in their own countries, so it is possible the Paris attacks were a spontaneous reaction to this.
While it is still too early to reach a definitive conclusion on which organisation, if any, was behind the Paris attacks, the most likely explanation at this stage is that despite the connections with global jihadist networks this was primarily the work of the three individuals themselves, helped by accomplices still being sought, all done with the encouragement, possibly funding, but little direction from al-Qaeda and IS leaderships in Pakistan, Yemen or Syria.