The author of the study, Ken Katzman (full disclosure: a friend), then proceeds to summarize the view you see in 90% of US media stories you see on al-Qaeda:

In assessing capabilities, many believe that the Al Qaeda organization and its leadership are no longer as relevant to assessing the global Islamic terrorist threat as they were on September 11, 2001. Some believe U.S. and allied counter efforts have weakened Al Qaeda's central leadership structure and capabilities to the point where Al Qaeda serves more as inspiration than as an actual terrorism planning and execution hub. According to this view, the threat from Al Qaeda has been replaced by a threat from a number of loosely affiliated cells and groups that subscribe to Al Qaeda's ideology but have little, if any, contact with remaining Al Qaeda leaders. Those who take this view believe that catastrophic attacks similar to those on September 11, 2001 are unlikely because terrorist operations on that scale require a high degree of coordination.

This view is probably best (or at least coherently) summarized by the writings of Jason Burke, which I had previously described as follows:

... viewing the actual al-Qaeda organization as being limited to an exceedingly small number of people, the majority of whom were captured or killed when the US attacked Afghanistan. Al-Qaeda in Burke's mind is not an organization but a brand name adopted by governments to refer to the amorphous adherents of violent Islamic extremism. There is no coordinated global terrorist offensive against the US or the West with bin Laden and his lieutenants as its leaders, but rather the actions of isolated and unconnected groups of Islamic extremists with only the most peripheral of ties to the actual al-Qaeda organization. Because al-Qaeda is an idea rather than organization, attempting to destroy it militarily is nothing short of folly. You can't kill an idea and the US attempt to do so is only serving to create a stronger following for it. I should also add that Juan Cole and many other academics and analysts (as well as investigative journalists such as Seymour Hersh) have been heavily influenced by the "Burkean" view in their own conceptions of al-Qaeda.

Now this certainly isn't anything resembling the popular conception of al-Qaeda, which I view as a good thing because I disagree with this type of analysis. Nor is it as universally popular in counter-terrorism, law enforcement, and intelligence circles as all the media coverage this view has gotten over the last 2 years might lead the unthinking observer to believe.

Katzman then proceeds to summarize the parallel view of al-Qaeda, which I have termed "Gunaratnan" after Sri Lankan counter-terrorism expert Rohan Gunaratna:

An alternate view is that the remaining Al Qaeda leadership remains in contact with, and possibly even in control of numerous Islamic militant cells and groups that continue to commit acts of terrorism, such as the July 7, 2005 bombings of the London underground transportation system. According to those who subscribe to this view, Al Qaeda as an organization has not been weakened to the degree that some Administration officials assert, and the global effort against Islamic terrorism would benefit significantly from finding and capturing Al Qaeda founder Osama bin Laden and his top associate, Ayman al-Zawahiri. Subscribers to this view believe that a coordinated attack on the scale of September 11 should not be ruled out because the remaining Al Qaeda structure is sufficiently well-organized to conduct an effort of that magnitude.

This pretty much encapsulates my own view as well as those of Dr. Gunaratna. While neither Burke nor Gunaratna were either the first or the last scholars to produce serious books on al-Qaeda, they still have the virtue of being the first people to my knowledge to set up a coherent narrative of the organization. Accepting that, whichever of these views are accurate is probably something that needs to be done if we want to defeat al-Qaeda, since the tactics that are employed against an ideology are quite different from those used against an organization. Interestingly, much of the armchair punditry surrounding al-Qaeda is, on average (as it varies from pundit to pundit), usually a reverse of what one might expect it to be, with left-leaning experts adopting a Burkean view and right-wingers a Gunaratnan. My own suspicion is that at least part of these differences have to do with how people here in the US feel concerning the use of military action as a solution to terrorism, but that is perhaps a discussion best reserved for another time.

Katzman then provides a brief overview of Osama bin Laden and al-Qaeda, including an interesting figure that the proto al-Qaeda MAK already had a network of between 10-20,000 members by 1988. Having finished his overview, he then touches on speculation concerning bin Laden and al-Zawahiri's location:

However, bin Laden and Zawahiri are not widely believed to be in Afghanistan proper; they reportedly escaped from their redoubt in the Tora Bora mountains (near the city of Khost) during the war and, according to most assessments, fled into Pakistan. Central Intelligence Agency paramilitary officers and other U.S. personnel (some as contractors) in Pakistan are dedicated to this search, assisting Pakistani forces and agents. Acting on the assumption that bin Laden and Zawahiri are in remote areas of Pakistan rather than in or around urban areas, in March 2004, Pakistan deployed about 70,000 troops against suspected Al Qaeda hiding places in the South Waziristan region, but failed to find the two, or any other major Al Qaeda figures. Current Pakistani military operations are centered around North Waziristan. There are very few indications of their whereabouts, but, in Time Magazine’s June 27, 2005 issue, Director of Central Intelligence Porter Goss said that the United States had an “excellent idea” where bin Laden was, but he did not specify any exact location.

White House spokesman Scott McLellan subsequently clarified the Goss comment to reflect less certainty than Goss indicated. Some experts believe the two might be in settled areas, perhaps even a large Pakistani city. The videotaped statements by the two, released over the past six months, appear to demonstrate that they have access to technology and physical infrastructure. Many of the 15 top Al Qaeda operatives captured or killed since September 11 — of the 37 such operatives identified after September 11 — have been found in urban areas. These include number three leader Mohammad Atef, killed in Kabul, Afghanistan by U.S. Predator; September 11 planner Khalid Shaikh Mohammed, arrested by Pakistani agents near Rawalpindi; key recruiter and planner Abu Zubaydah, arrested by Pakistani agents in Faisalabad; September 11 plotter Ramzi bin al-Shibh, arrested by Pakistani agents in Karachi; and Abu Faraj al-Libbi, arrested by Pakistani forces near Peshawar in May 2005. Al Libbi is perceived as an operative who has risen in the organization since September 11, but some question al-Libbi’s seniority and importance to recent Al Qaeda plotting.

Al-Libbi, as noted before, was not the al-Qaeda third-in-command but rather the head of al-Qaeda in Pakistan. That's certainly an important position within the network, but not nearly as high up as some tried to claim at the time of his capture. I would also point out that the Pakistani military operations in 2004, once they were honest about it, were not focused so much focused on al-Zawahiri as they were a trio (2 IMU leaders and a Chechen) of senior al-Qaeda leaders based in northern Pakistan.

Another point that needs to be stressed time and time again is that bin Laden and al-Zawahiri, wherever they are, are not living in a cave but rather have access to both modern video equipment and probably CNN International, BBC World, and al-Jazeera on satellite TV as well. Also, contra the mantra that they are removed from any type of command and control operations, both men are apparently in control of a very effective smuggling operation that has enabled them to send a regular series of messages back and forth to al-Jazeera without being traced by US intelligence.

Katzman isn't about to ignore the element in the room either:

Some other senior figures are apparently beyond U.S. reach. Al Qaeda spokesman Suleiman Abu Ghaith, operations planner Sayf al-Adl, and bin Laden’s son Saad are believed to be in Iran. Iran has acknowledged publicly that it has some senior Al Qaeda figures “in custody” — without naming them specifically — but Iran has refused to transfer them to their countries of origin for interrogation and trial. Many doubt the degree of constraint, if any, that Iran has placed on them, and the Bush Administration has publicly alleged that the three were responsible for planning the May 2003 suicide attacks on a housing complex in Riyadh, Saudi Arabia. If true, this would suggest that the three are in contact with Al Qaeda operatives outside Iran. Some might argue that, if these three senior figures are able to communicate with bin Laden and Zawahiri, a major portion of the core of the Al Qaeda leadership as it existed on September 11, 2001 is still operating and possibly in control of ongoing operations. Those who take this view tend to believe that the United States
should exert greater efforts to capture bin Laden and Zawahiri on the grounds that they remain pivotal leadership figures and that their capture would greatly deflate the organization.

And just going off of press reports, we might well add any number of other senior al-Qaeda leaders who have been cited as being in or having been in Iran. The cynical part of me tends to lean towards the view that many of those in government who want to downplay the organizational nature of al-Qaeda do so because, especially given the current situation in Iraq, they are very much afraid of what would happen were everything that is now known about al-Qaeda/Iran become part of the regular public and political discourse. My own view is that this is going to happen sooner or later, especially if there's another attack, and that we might as well start talking about this now rather than trying to kick it down the road as far as possible, which appears to be the current European approach as far as its negotiations with Iran over its nuclear program are concerned.

Katzman then shifts his summary towards a modified Burkean approach, reflected in the State Department's Patterns of Global Terrorism:

Another view is that the Al Qaeda organization, as it still exists, is less central to the overall Islamic terrorist threat faced by the United States than it was at the time of the September 11 attacks. Reflecting this view, the State Department report on terrorism for 2004 (p. 7) says, as do many experts, that:

Al Qaeda’s evolution since September 11 could change the nature of the threat posed by the organization. Many believe that the weakening of central direction renders Al Qaeda less able to conduct catastrophic attacks inside the United States because its diffusion limits its ability to orchestrate complicated, coordinated plots similar to the September 11, 2001 attacks.

And then we shift from the analytical to the political:

The Bush Administration asserts that the absence of attacks inside the United States since September 11 demonstrates that the main thrust of Administration policy is succeeding. However, it could be argued that more autonomous affiliates might be better able to adapt attacks to local conditions and goals, making them a major collective threat.

To which I would add that you can probably tell what an American thinks on this note by how they voted last November. This isn't to say that either argument is pure hackery, but it makes sense that those who believe that the administration is doing a good job voted in favor of it with the inverse for those who think it's doing a bad job.

And then a modified Burkean view, this one focusing on the role of the second generation of al-Qaeda leaders. According to this view, al-Qaeda might have been the structured organization described by Gunaratna and others before 9/11, but it is no more:

Younger Al Qaeda figures, some of whom fled the Afghanistan battlefield, are said to be emerging as major planners, and these activists apparently see Al Qaeda as inspiration rather than as a structured organization. According to this view, bin Laden and Zawahiri are far less operationally relevant than they were at the time of September 11 and U.S. and allied counter-terrorist efforts might be better spent on countering the ideology that is promoted by Al Qaeda. Experts have advanced some ideas for doing so, including enhanced U.S. public diplomacy and stepped up efforts to engage moderate Islamic clerics in the Islamic world to enlist them in an effort to de-legitimize Al Qaeda’s tactics.

Katzman then stresses the fact that al-Qaeda is as much a coalition of terrorist groups as it is a single organization, a point that has been made repeatedly by Gunaratna, Clarke, and Scheuer among others:

Some experts believe that Al Qaeda is not significantly more diffuse than it was prior to the September 11 attacks. Al Qaeda has always been more a coalition of different groups than a unified structure, many argue, and it has been this diversity that gives Al Qaeda global reach — the ability to act in many different places and to pose a multiplicity of hard-to-predict threats. In most cases, the degree of involvement, if any, by bin Laden, Zawahiri, or other known Al Qaeda leaders in the operations of these diverse groups has never been precisely known. Some major groups were part of the Al Qaeda coalition before September 11, and most remain active and still associated with Al Qaeda today, to varying degrees ...

I stress the "has never been precisely known," because this is an important distinction from the often-repeated meme that many of these groups' allegiance to al-Qaeda is merely symbolic or a sign of close ideological kinship. This is not the same as an absolute certainty of operational connections or command and control, but it by no means precludes them. The major affiliate groups listed by Katzman are al-Gamaa Islamiyyah, Egyptian Islamic Jihad, the Algerian GIA and GSPC, the Islamic Movement of Uzbekistan, Jemaah Islamiyah, the Libyan Islamic Fighting Group, the Pakistani quartet of Harakat ul-Mujahideen (HuM), Jaish-e-Mohammed (JeM), Lashkar-e-Taiba (LeT), and Lashkar-e-Jhangvi (LeJ), and the Lebanese Asbat al-Ansar.

Katzman then lists Ansar al-Islam (later Ansar al-Sunnah) and al-Qaeda in Iraq as two new major al-Qaeda affiliate groups that have recently come to the fore over the last several years.

The issue of whether the war in Iraq has helped or hurt al-Qaeda is then discussed:

Although Zarqawi reputedly sees himself as a potential leader of Islamic forces in his own right, in 2004 he formally swore fealty to bin Laden and affiliated with Al Qaeda. Some maintain that Zarqawi is successfully stoking Muslim opposition to the U.S. intervention in Iraq to recruit Muslim fighters not only for combat in Iraq, but possibly also for terrorist operations in other Western countries and in other Middle Eastern countries, including his native Jordan. In this view, which reportedly is shared by the Central Intelligence Agency in a recent assessment, the U.S. involvement in Iraq has strengthened rather than weakened groups connected to or influenced by Al Qaeda. The reputed CIA assessment says that Iraq is now playing a role similar to that of Afghanistan during the Soviet occupation - a training ground for Islamic militants who might travel elsewhere after the Iraq conflict winds down.

A note is then made that some of Zarqawi's activities appear to bolster the Gunaratnan analysis with respect to al-Qaeda's structure:

Zarqawi’s formal affiliation with bin Laden gives some support to the view that the remaining Al Qaeda leaders might be trying to rebuild the organizational structure of Al Qaeda before its leadership was ousted from Afghanistan in late 2001.

Katzman then turns to the lesser or emerging al-Qaeda affiliate groups: the Islamic Army of Yemen, Gulbuddin Hekmatyar's Hizb-e-Islam, the Moroccan Islamic Combatant Group that carried out the 3/11 bombings in Spain, and al-Qaeda fi al-Jazeera, more commonly known as al-Qaeda in Saudi Arabia.

More murky among experts is the issue of how strong al-Qaeda is in East Africa:

Depending on the outcome of investigations, some of the bombings and attempted bombings of the London transportation system in July 2005 might support the belief in the Administration and among some outside experts that there is a growing Al Qaeda presence in East Africa. Two of the suspects arrested in the failed July 21 bombings were of East African origin, and there had been longstanding fears among Western intelligence agencies that Al Qaeda might be recruiting or controlling cells consisting of East Africans for operations in Europe or elsewhere. Al Qaeda was allegedly responsible for the bombing of an Israeli-owned hotel and the related firing (and near
miss) of shoulder-fired missiles at an Israeli passenger aircraft, both in Mombasa, Kenya in November 2002. Reflecting Administration fears about Al Qaeda’s expansion in Africa, the U.S. military has begun a program to train the militaries of nine African nations to prevent infiltration by terrorist groups, particularly Al Qaeda.

Though Katzman correctly notes that there is a lot we still don't know about the attacks of this summer:

It is not yet known to what extent, if any, the July 21 bombers might have had links to the bombers who set off the July 7 explosions in London that killed 52 persons. Some of those alleged perpetrators (who died in the bombings) were British-born but of South Asian origin, but some press reports indicate that the July 7 and the July 21 bombers might have visited Pakistan simultaneously, suggesting a possible tie between them and perhaps to the Al Qaeda leadership that is thought to be in Pakistan. A claim of responsibility for the July 7 attacks came from a previously little known group called “The Secret Organization of Al Qaeda in Europe,” a name that suggest some linkage to or affinity with Al Qaeda. Two days after the failed July 21 London attacks, suicide bombers in Sharm el-Sheikh, Egypt killed 88 in attacks on a hotel district; an investigation is under way to determine linkages, if any, of those attacks to Al Qaeda, to radical Islamist groups in Egypt, or
to October 2004 bombings in Taba, Egypt that killed 34 persons.

In conclusion, Katzman notes that the absence of a definitive agreement of what al-Qaeda is leads to considerable difficulty in determining how to fight it, focusing on the Burkean and Gunaratnan views and gives us some idea of the stakes with respect to Iraq:

The assessment of the degree and character of the threat posed by the Al Qaeda organization might suggest strategies for combating it. Those who believe that Al Qaeda as an organization is marginal to the overall global Islamist threat might focus on such policy objectives as addressing regional conflicts, promoting democracy in the Arab world, cooperating with regional governments to prevent terrorism financing and terrorist infiltration, and improving public diplomacy to better explain U.S. policies in the Middle East. On the other hand, some who believe that Al Qaeda remains central to the Islamist terrorism threat might tend to recommend policies that focus on finding, combating, and arresting Al Qaeda leaders and operatives that are still at large. Many believe that, no matter the structure and capabilities of Al Qaeda, stabilizing Iraq will likely be crucial to reducing the recruitment of militants willing to conduct acts of terrorism against the United States and its allies.

He then airs a third view that, while uncommon in the US, is the standard way in which discussion of terrorism is conducted by the political class in much of Europe. You can also find this in the pre-9/11 writings of such notables as Larry Johnson and Paul Pillar.

Others believe that the Al Qaeda and global Islamic terrorist threat is difficult to assess, no matter how much intelligence is shared and gathered, and that combating Al Qaeda and its affiliates abroad could have only partial success. Those who take this view tend to believe that U.S. counter-efforts should focus more intently on homeland security, stressing such measures as improving airline security, establishing enhanced security measures for passenger train travel, and expanding security of U.S. ports. Some tend to favor additional powers for law enforcement to investigate potential Islamist cells in the United States. The latter suggestions often trigger debate from civil liberties and American Muslim organizations who believe that such measures will inevitably impinge on the civil liberties of Arab and Muslim Americans through profiling and other investigative techniques.

These are all good steps in and of themselves, but here's the problem: this was the US counter-terrorism strategy prior to 9/11. Regarding al-Qaeda as a law enforcement rather than a counter-insurgency dilemma is a fool's errand, as Scheuer can tell you. Part of the attractiveness of the law enforcement approach to terrorism is the belief that this is a problem that is limited to the Middle East and can be contained through a combination of an isolationist foreign policy and a "Fortress America" approach to foreign policy. The US learned on 9/11 that this approach is not a feasible one and today neither major political party advocates such an approach. It remains to be seen whether Europe will become more like America in this regard or the inverse, but it still remains an ongoing concern of mine today, 4 years after the attacks.

Time will tell.