This undated photo released late Sunday by Greece's migration policy ministry shows a document issued to 25-year old Ahmad Almohammad, holder of a Syrian passport found near a dead assailant in the scene of a Paris attack Friday. The document was issued on Sunday, Oct. 4, by authorities on the Greek island of Leros, where the man arrived a day earlier on a frail boat carrying migrants over from Turkey. (Greek Migration Policy Ministry via AP)

A key bit of evidence that emerged in the investigation of the Paris terror attacks, which saw at least 129 people killed on Friday, is a supposed Syrian passport found near the body of one of the slain assailants. It bore the name of a Syrian national who apparently transited through Greece in early October. The document seemed to be an important clue in the untangling of the terror plot.

But more than that, it sparked a larger debate: Could one of the terrorists have been a Syrian refugee?

The prospect of Islamist infiltration through the current refugee influx in Europe has spooked politicians on both sides of the Atlantic, with a slate of Republican governors and presidential candidates in the United States pointing to the terror attacks as reason to bar entry to all Syrian refugees.

Here's what we do and don't know about the rumors of Syrian refugee involvement in the Paris terror attacks.

THE PASSPORT IS FAKE: Authorities in multiple countries are pretty certain that the passport, found near the body of an unidentified attacker who died during his suicide assault of France's national soccer stadium, is fake. It carried the name of "Ahmad Almohammad," a 25-year-old Syrian. French officials have indicated that Almohammad was a loyalist soldier in the regime of Syrian President Bashar al-Assad and died a few months ago.

On Tuesday, Serbian police arrested another man at a refugee camp carrying a passport with the exact same details. It's not clear at all if he has any connection to the case, other than having used the same shadowy process of obtaining a forged Syrian passport. There is a great deal of precedent for migrants pretending to be Syrians to gain safer passage and sanctuary in Europe.

Thomas de Maiziere, Germany's interior minister, suggested on Tuesday that the fake passport found at the bombing site could have been part of an Islamic State attempt to create a "false trail."

FINGERPRINTS: The passport, or at least a copy of the passport, was shown to Greek officials by someone carrying it on the island of Leros, where thousands of Syrian refugees and other migrants have made landfall this year. On Oct. 4, the Greek ministry for migration policy issued a document (pictured above) to "Ahmad Almohammad" that would protect him from deportation for the next six months.

It's not totally clear whether the fingerprints there match those of the unidentified assailant who was apparently carrying this fake Syrian passport, though a French prosecutor said on Monday that there "similarities" between the prints of the suicide bomber and those found on the Greek document. And if they do indeed match, it still isn't clear if the man in question was a Syrian national.

On Tuesday, French authorities circulated a flier seeking help to identify the unknown attacker.

IDENTIFIED ASSAILANTS ARE E.U. NATIONALS: Although the Paris terror attacks appear to have been partially planned or coordinated by Islamic State operatives in the Middle East, all the identified assailants are so far citizens of European Union countries. This suggests that their radicalization was likely homegrown on the continent, and not imported via an exodus of beleaguered Syrian refugees.

According to the Post's own graphic tracking the case, three out of the eight known assailants remain unidentified. Only one man is known to be alive. French officials confirmed on Tuesday that they were looking for a ninth suspect connected to the attacks.

Authorities say as many as 20 people may have been involved in the plot to attack Paris. Here's what we know about them so far. (Gillian Brockell/The Washington Post)

Related on WorldViews

The Islamic State wants you to hate refugees

5 stories you really need to read to understand the Islamic State