When the National September 11 Memorial & Museum opens Thursday, we will finally have a national institution dedicated to exploring the effects of the tragic events of the 9/11 terrorist attacks.

The impact of that day on U.S. legal institutions, however, remains a work in progress. The federal court system has proven remarkably adept at handling the hundreds of criminal terrorism cases filed since Sept. 11, 2001. But the polarized politics of terrorism has left Washington paralyzed when it comes to handling the cases of dozens of indefinite detainees still imprisoned at Guantanamo Bay, Cuba.

In New York last week, the U.S. government rested its case against the one-eyed, hook-limbed Sheikh Abu Hamza al Masri, on trial in federal court on terrorism charges. For weeks spectators were treated to a string of government informants, including confessed terrorism supporters, who seemed to have no qualms about taking the witness stand and incriminating the fiery preacher the government says inspired and directed lethal acts against Americans. In April, another extremist cleric, Suleiman Abu Ghaith, was convicted based on similar evidence.

In Washington, however, with the National Defense Authorization Act now pending in Congress, lawmakers and policy experts are again debating what to do about the men the United States has indefinitely detained for alleged terrorist activity at Guantanamo Bay. The question is growing more urgent as Washington prepares to withdraw its combat troops from Afghanistan by the end of this year — officially ending the war there. That arguably ends the president’s authority to detain prisoners under the laws of war as well.

President Barack Obama reiterated in January his desire to close the notorious Guantanamo prison by the end of this year. Even among those who agree it should close, a surprising number of lawmakers and policy analysts seem to believe that may require creating a new indefinite detention scheme for suspected terrorists here in the United States.

Supporters of these proposals highlight the allegedly intractable problem of some 45 detainees at Guantanamo, and potentially more, whom the Obama administration has insisted since 2009 cannot be convicted on criminal charges, yet are nonetheless too dangerous to release.

The effect is to create a group of people secretly deemed by the government to be detainable beyond the reach of the law. So should Congress create a new law to allow that?

For anyone who’s watched terrorism trials unfold in New York, the underlying premise — that these men have committed crimes yet cannot be prosecuted — seems hard to believe. The government has managed to draw a broad range of suspected or convicted terrorists out of the shadows when needed to testify on everything from military-style training in Afghanistan to the testing of poison gas on small animals. At least one witness even testified for the government by videotape from another country — to avoid a U.S. indictment.

It’s therefore hard to believe the government couldn’t find people to provide enough evidence to prosecute these 45 alleged al Qaeda or Taliban fighters. If, indeed, they’ve done anything wrong.

Under federal law, when it comes to terrorism, “wrong” is broad concept. Take the case of Suleiman Abu Ghaith, the extremist Muslim cleric convicted last month of conspiring with al Qaeda to kill Americans and providing material support for terrorism. A prominent religious figure in Kuwait who moved his family to Afghanistan after he lost his job at home, he’ll likely face life in prison when he’s sentenced in September for delivering a handful of speeches praising al Qaeda activities in the name of Allah.

Or consider Syed Hashmi, the former Brooklyn College student who pled guilty to material support for terrorism, after he loaned $300 to a friend staying with him and let his friend store ponchos and socks in his London apartment. The friend planned on delivering the items to al Qaeda in Afghanistan.

Both men were convicted based on evidence provided by government informants previously convicted on terror-related charges. Such informants have a huge incentive to provide evidence against others charged with terror-related crimes in the hopes of winning leniency in their sentencing, or in some cases avoiding prosecution altogether.

The Justice Department has prosecuted hundreds of terrorism cases since the September 11 attacks. It’s hard to imagine the government hasn’t gathered enough evidence in those investigations to be able to link any actually guilty men at Guantanamo to terrorism.

Consider what the men at Guantanamo are accused of. Ghaleb Nassar al-Bihani is typical. At a recent periodic review board hearing at Guantanamo, the government claimed Bihani attended al Qaeda and Taliban-affiliated training camps “where he received in-depth instruction on the use of small arms and probably anti-aircraft weapons, lEDs, mortars, and landmines.” He then supposedly “operated on the frontlines against the [U.S.-supported] Northern Alliance in various capacities.”

If the government continues to detain Bihani under the laws of war — then it has to continue to be in that war. When the war in Afghanistan is over, that will likely be a hard case to make.

To prosecute Bihani under the federal terrorism laws, on the other hand, should be easy. If the government can demonstrate he attended the al Farouq training camp to train al Qaeda adherents to kill Americans, as it claims, that’s enough to convict him for material support of terrorism. If he “operated on the frontlines” with al Qaeda, as the government also claims, he’s guilty of conspiracy to kill Americans as well. Never mind that the United States was fighting and killing Afghans at the time — the U.S. position has always been that al Qaeda fighters were “unlawful enemy combatants” and aren’t entitled to combat immunity from criminal prosecution.

Bihani, for his part, denies fighting with al Qaeda or the Taliban. He does admit, however, to being “an assistant cook” in one group fighting the United States. That in itself is likely enough to convict him for material support.

Though Congress extended the reach of the material support law in 2004 to include anyone who supported any terrorism anywhere, the earlier 1996 law banning material support for terrorists would still seem to cover the conduct of someone like Bihani, who supported terrorist groups aiming to kill Americans. He also doesn’t deny receiving training. He does deny, though, that he poses any threat to the United States. Yet, the U.S. government still says it’s concerned about sending him back to his home country of Yemen because he has family members allied with Al Qaeda in the Arabian Peninsula. He himself doesn’t want to return to Yemen, or to fighting, he says.

Such cases offer two choices. First, the government could prosecute Bihani in the United States, calling up some of its army of convicted terrorists who could testify having seen him at the Afghanistan training camp and assisting al Qaeda operatives in their campaign to kill Americans. Or, second, the government could decide prosecution is unnecessary and send Bihani to a third country where he could participate in some sort of parole or surveillance program — so he won’t pose a terrorist threat.

The claim that there are dozens of men at Guantanamo who cannot be tried and are also too dangerous to release is a premise we wouldn’t accept from any other country. Before Washington policymakers buy into that idea, the government should be required to demonstrate publicly what evidence it has against these men, and whether and why that evidence is inadmissible in a court of law.

Federal judges have typically bent over backward to allow these prosecutions to go forward. Federal District Court Judge Lewis Kaplan, for example, ruled in 2010 that the delay in bringing former Guantanamo detainee Ahmed Ghailani to trial for the 1998 U.S. embassy bombings in East Africa was not a violation of his constitutional right to a speedy trial. He decided that the laws of war allowed the government to detain Ghailani and interrogate him — first in secret CIA custody and then at Guantanamo Bay — for five years until he was brought to a U.S. court in 2009. An appeals court last year affirmed that ruling.

If the only evidence against these men was derived from torture, then that evidence should be inadmissible — in part because it’s not reliable. But then, it’s not a reliable basis upon which to detain them indefinitely either.

The objection to trying alleged terrorists in federal courts is often a visceral one. But it’s not sustainable. As Kaplan wrote in his 2010 decision permitting the prosecution of Ghailani:

The court understands that there are those who object to alleged terrorists, especially non-citizens, being afforded rights that are enjoyed by U.S. citizens. Their anger at wanton terrorist attacks is understandable. Their conclusion, however, is unacceptable in a country that adheres to the rule of law.

Similarly, to continue to detain indefinitely alleged “combatants” after the United States withdraws its combat troops from the war they fought in is to flout the rule of law. Even if Congress creates a new (and constitutionally questionable) law allowing it, it may well violate the international laws of war.

If these men are guilty of supporting or conspiring in terrorism, the government may prosecute them for that. If they’re not, then the clock is ticking: It will soon have to let them go.

PHOTO (TOP): Detainees in orange jumpsuits sit in a holding area under the watchful eyes of military police during in-processing to the temporary detention facility at Camp X-Ray of Naval Base Guantanamo Bay, January 11, 2002. REUTERS/Stringer/Files

PHOTO (INSERT 1): A detainee is carried by military police after being interrogated by officials at Camp X-Ray at the U.S. Naval Base at Guantanamo Bay, Cuba, February 6, 2002. REUTERS Marc Serota

PHOTO (INSERT 2) A boy holds a picture of his uncle, who is detained in Guantanamo Bay, as riot policemen (background) stand guard during a protest demanding the release of Guantanamo detainees, outside the U.S. embassy in Sanaa, January 11, 2014. REUTERS/Mohamed al-Sayaghi

PHOTO (INSERT 3): An artist sketch shows Suleiman Abu Ghaith, a son-in-law of Osama bin Laden and one of the highest-ranking al Qaeda figures to be brought to the United States to face a civilian trial, at a hearing in a Manhattan federal court in New York April 8, 2013. REUTERS/Jane Rosenberg

PHOTO (INSERT 4): No photography signs are posted on the fence surrounding Camp Delta at the U.S. Naval Base at Guantanamo Bay, March 6, 2013. REUTERS/Bob Strong