Americans already inclined to see Pope Francis through a hermeneutic of suspicion might think the pontiff is delivering what Italians would call a disprezzo today, more or less a sign of disrespect, by receiving the leader of their great Cold War rival on the very day Americans celebrate their independence.

Of course, the pope’s appointment calendar isn’t set on the basis of such considerations. Russian President Vladimir Putin is in Italy July 4 for a one-day state visit at the invitation of Prime Minister Giuseppe Conti, and when heads of state visit Italy they’re also expected to drop in on the pontiff. Given the protocol involved, if either Putin or Francis were somehow to wiggle out from the appointment, that would be seen as the real disprezzo.

Anyway, Putin and U.S. President Donald Trump are essentially BFFs, so there’s no sense in which the American leader could reasonably feel slighted. For the record, Putin will also meet Italian President Sergio Mattarella while he’s in town.

Today’s tête-à-tête is the third encounter between Putin and Francis, and, in typical fashion, most global media outlets are giving it short shrift in favor of a focus on perceived tensions between Russia and Italy’s Deputy Prime Minister Matteo Salvini, the de facto center of power in the Italian government and the presumptive leader along with Marine Le Pen in France of Europe’s burgeoning right-wing populist movements.

(Last October, Salvini said - perhaps jokingly, perhaps not, one can rarely tell - that people who did business with Russia were “the worst criminals on Earth,” helping to fund a country that has spies who “go around Europe poisoning random people.”)

However, there’s a strong case to be made that the session with Francis is the most potentially consequential stop on Putin’s itinerary today.

Here’s why.

At the moment, especially after Trump and North Korean leader Kim Jong-un appeared to turn a new leaf in their relationship, perhaps the clearest threat to global peace and stability is the tension between the U.S. and Iran.

On Monday, the White House asserted that Iran had violated a 2015 deal on its nuclear program before it even existed, which substantively amounted to an expression of distrust but, as a matter of strict logic, was nonsensical. (By definition, it’s impossible to break a deal that hasn’t yet been made.) The Iranian foreign minister took to Twitter with a one-word response: “Seriously?”

The current conflict dates to last year, when Trump pulled out of the nuclear deal and re-imposed sanctions on Tehran. Late last month, Trump declared that the U.S. military was “cocked and loaded” for strikes against Iran in retaliation for shooting down an American surveillance drone until he called it off at the last minute over concerns about the potential loss of life.

Iran has announced that it will intentionally surpass limits on its enriched uranium supplies in that 2015 deal, and also warned that time is running out to save the accord. If there are two figures on the global stage who might be in a position to help steer Iran away from a cycle of conflict, arguably Putin and Francis are the two best candidates.

Russia is Iran’s major patron and ally in the Middle East, and the Vatican has long enjoyed positive relations with Tehran. In truth the Vatican and Moscow are already in sync on several fronts, from Syria to Venezuela.

Moreover, Iranian President Hassan Rouhani comes from the ijtihad tradition in Shi’a Islam, which emphasizes the use of individual human reason over legal conformity, implying creativity and adaptation in applying religious law to changing situations - though the analogy is inexact, it’s sort of the closest thing Islam has to the pope’s own Jesuit order in Catholicism.

Should Putin and Francis reach a meeting of the minds on Iran, it’s possible that Rouhani and the rest of the Iranian leadership might be open to an overture. Aleksandr Avdeev, Russia’s ambassador to the Vatican, recently told Ogonek magazine that “the situation in Iran” is on the agenda for Putin and the pontiff today.

(In all honesty, if there is some heavy lifting on Iran today, most it likely won’t happen when Putin speaks to Francis but in his session afterwards with Italian Cardinal Pietro Parolin. Every head of state who visits the pope is also expected to see the Vatican’s Secretary of State, and those are usually the meetings where the diplomatic and political sausage is ground.)

Of course it takes two to tango, so an equally pressing question is whether such a diplomatic initiative might be looked upon with favor by the White House. Aside from the fact Putin would be involved, there are at least two other reasons to believe there might be an opening.

First, fresh off his encounter with Kim, Trump may have developed a taste for perceived diplomatic breakthroughs. Second, since Trump’s going to need at least some share of the Catholic vote in 2020, he might be in a humor to be perceived as collaborating with the pope on a matter of global consequence.

There are all kinds of reasons why a Putin/Francis intersection on Iran might not happen, starting with the fact that at the same time Francis is meeting the Russian leader he’s also receiving the leadership of the Greek Catholic Church in Ukraine, which has been hugely critical of Russia’s military intervention in the eastern part of their country. The Putin/Francis session could be dominated by discussion of Ukraine, leaving little space for other matters.

Still, the mere prospect of movement on Iran at least makes today interesting - because, let’s face it, it’s hard to imagine anything world-changing is likely to result from Putin’s encounters with either Conte or Mattarella.