Russian President Vladimir Putin. (Alexander Zemlianichenko/AP)

Robby Mook, the manager of Hillary Clinton's campaign, made a remarkable claim during an appearance on CNN's "State of the Union" on Sunday. Mook and host Jake Tapper were discussing the leak of Democratic National Committee emails.

"What's disturbing to us is that experts are telling us that Russian state actors broke into the [DNC], stole these emails," Mook said. "And other experts are now saying that the Russians are releasing these emails for the purpose of actually helping Donald Trump. I don't think it's coincidental that these emails were released on the eve of our convention here. That's disturbing. I think we need to be concerned about that."

Mook went on to note other ways in which Trump seems to be unusually sympathetic to Russia or Russian President Vladimir Putin, saying, "When you put all this together, it's a disturbing picture. I think voters need to reflect on that."

This is part of an emerging thread in the political conversation: Putin is exerting what influence he has available to help Trump's bid for the presidency. It's overlaid with another thread: that Trump is doing things that demonstrate an unusual willingness to acquiesce to Russian interests. Those are separate ideas, for which advocates point to different evidence — and the evidence provided for each varies in credibility.

Let's evaluate.

Are Putin and the Russians acting to support Trump's candidacy?

We'll start with the emails.

Last month, The Post reported that the breach of the DNC was linked to Russian state actors. A firm hired by the DNC to track intrusions, CloudStrike, "identified two separate hacker groups, both working for the Russian government, that had infiltrated the network." The company had analyzed other infiltrations from the groups over the past several years. (Ties to Russian hackers have since been corroborated.) Once inside the DNC, one group looked at email and chat over a long period; another targeted opposition files on Trump.

On Friday, about 20,000 of those emails ended up on WikiLeaks. It's not clear how WikiLeaks got the documents, but a hacker identifying himself as Guccifer 2.0 claimed credit on Twitter. The name is a reference to Guccifer, the Romanian hacker who got into Clinton adviser Sidney Blumenthal's email system several years ago and who claims to have hacked Clinton's. He was arrested and pleaded guilty to criminal charges in May.

When Vice talked to Guccifer 2.0 in June, he also claimed to be Romanian. He took great pains to argue that he had acted alone. But "when we asked him to explain to us how he hacked into the DNC in Romanian, he seemed to stall us, and said he didn’t want to 'waste' his time doing that," Vice reported. "The few short sentences he sent in Romanian were filled with mistakes, according to several Romanian native speakers. The hacker said he left Russian metadata in the leaked documents as his personal 'watermark.'"

Caputo worked for the Trump campaign until June.

Russia's facility with online disruption is established: It reportedly has a vast, sometimes informal operation of people who are employed to wreak havoc online. Last year, the New York Times's Adrian Chen explored the workings of "the Internet Research Agency," as it's known. Hundreds of employees are paid to mix falsehoods with truth on social media to mislead and misinform. "Russia’s information war might be thought of as the biggest trolling operation in history," Chen wrote, "and its target is nothing less than the utility of the Internet as a democratic space."

In May, the Times followed up with a story about the harassment of a journalist who wrote about Russia's attempts to undermine the North Atlantic Treaty Organization. "Pro-Russian voices have become such a noisy and disruptive presence that both NATO and the European Union have set up special units to combat what they see as a growing threat not only to civil discourse but to the well-being of Europe’s democratic order and even to its security," the Times wrote.

"There appears to be some kind of alignment across social media between these extremist groups in the West and the Russian groups," the New America Foundation's Peter Singer told the Sydney Morning Herald in June, as part of an exploration of how online pro-Russia activity overlapped with pro-Trump advocacy. It's not clear that the Russian agency is directly involved in pushing for Trump online, though there is evidence that some of his social media support originates from bots.

The timing of the WikiLeaks release, coming immediately before Clinton's announcement of her vice presidential pick and the Democratic convention, is one reason that Mook and others suggest that the ultimate goal is political disruption.

At Slate, Frank Foer points to a pattern of behavior by the Russians. "Putin runs stealth efforts on behalf of politicians who rail against the European Union and want to push away from NATO. He’s been a patron of Golden Dawn in Greece, Ataka in Bulgaria, and Jobbik in Hungary," Foer wrote. He quotes Vice President Biden from last year:

[T]he Kremlin is working hard to buy off and co-opt European political forces, funding both right wing and left wing anti-systemic parties throughout Europe. President Putin sees such political force as forces as useful tools to be manipulated, to create cracks in the European body politic which he can then exploit.

"Anti-systemic" is a good way to describe the Republican nominee for president.

Is Trump unusually sympathetic to Putin and Russian interests?

For all of the attention that the Republican National Convention got, one incident flew largely under the radar. During the party's discussion over its 2016 platform, the Trump campaign got directly involved in shaping the official Republican position on Ukraine.

"Diana Denman, a platform committee member from Texas who was a Ted Cruz supporter, proposed a platform amendment that would call for maintaining or increasing sanctions against Russia, increasing aid for Ukraine and 'providing lethal defensive weapons' to the Ukrainian military," our Josh Rogin reported. "Trump staffers in the room, who are not delegates but are there to oversee the process, intervened. By working with pro-Trump delegates, they were able to get the issue tabled while they devised a method to roll back the language."

Fingers immediately pointed back to Trump's campaign manager, Paul Manafort. Manafort was employed for years as a lobbyist by the pro-Russian president of Ukraine who was ousted in the uprising of 2014. Manafort denied any connection.

That's only one connection between Trump and Russia. In June, we detailed the extent of the financial ties between Trump and Russia — and Trump and and Putin allies. "Russians make up a pretty disproportionate cross-section of a lot of our assets," Donald Trump Jr. said in a 2008 interview. "We see a lot of money pouring in from Russia."

Trump has repeatedly praised or excused Putin's strong-arm tactics and role in international affairs. In the wake of Putin's invasion of Crimea, Trump accused President Obama of being weak and praised the spike in popularity for Putin that resulted from the invasion.

He has repeatedly also shown willingness to make decisions that bolster Russia's international position. Last fall, Trump suggested that the fight in Syria be ceded to Russia. More recently, he suggested that the United States rethink its involvement in NATO and, in an interview with the Times, said he wouldn't necessarily honor America's commitment to protect Baltic states that are members of the organization and have grown tense at recent Russian threats.

The Republican nominee also embraced reports that Putin had called him "bright" (but not, as Trump relayed it, "brilliant"). MSNBC's Joe Scarborough in December pressed Trump on accepting praise from Putin, given that Putin "kills journalists that don't agree with him."

"Well," Trump replied, "I think that our country does plenty of killing, too."

There's clear benefit to Mook and the Democrats to tie Trump to Putin, a benefit that can't be ignored. Instead of talking about the contents of the emails, Clinton's allies would rather talk about how they were made public, understandably.

We don't yet know the extent to which the circumstantial outlines of sympathy and influence above are real. It does seem to be the case, though, that we can add questions about Russia’s role in our politics to the already-long lists of ways in which the 2016 campaign is exceptional.