At issue are the payments to two women who alleged sexual relationships with Trump before his running for president. In August 2016, Playboy model Karen McDougal reached an agreement with American Media Inc., publishers of the National Enquirer, that ensured she wouldn’t share her story about a lengthy relationship she’d engaged in with Trump. In October of that year, adult film actress Stormy Daniels received $130,000 to similarly stay quiet about a liaison that had occurred a decade before.

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Both of those agreements were facilitated by Cohen, as he admitted in court in August. Since Cohen was an agent of the Trump campaign — Cohen was a public surrogate on its behalf and, the Friday filing notes, had a campaign email address — neither payment could be considered an expenditure independent of the campaign but were, instead, campaign contributions in excess of federal limits. That one payment came from AMI meant that Cohen had solicited an illegal corporate contribution as well. Cohen pleaded guilty to two campaign-finance-related charges in August, saying in court that he’d undertaken the actions at Trump’s behest.

Cohen making that claim in court is one thing. The government making the same allegation in a court filing is another. And on Friday, the government made that allegation.

“With respect to both payments, Cohen acted with the intent to influence the 2016 presidential election,” the filing reads. “Cohen coordinated his actions with one or more members of the campaign, including through meetings and phone calls, about the fact, nature, and timing of the payments. In particular, and as Cohen himself has now admitted, with respect to both payments, he acted in coordination with and at the direction of Individual-1.”

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We know from the broader context of the document that “Individual-1″ is the person serving as president of the United States.

What’s more, the document explains that it isn’t only Cohen’s word that applies. Cohen recorded conversations between himself and others, including Trump, in which the payments were discussed.

“[A]fter Cohen caused the media company to make an illegal expenditure, in a secretly recorded meeting Cohen took credit for the payment and assured Individual-1 that he was ‘all over’ the transaction," the document reads. (That conversation was released earlier this year.) “And after making the payment to the second woman, and after Individual-1 was elected President, Cohen privately bragged to friends and reporters, including in recorded conversations, that he had made the payment to spare Individual-1 from damaging press and embarrassment.”

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Linking Trump to knowledge of the payment and the payment to the campaign is important. One of the defenses that might have been offered by Trump is that he regularly had his attorney pay off women to keep their stories quiet. The government filing indicates that AMI and Cohen discussed the company helping to make such payoffs as early as 2014. But the references to the rationale behind the payments in 2016 and the inclusion of the phrase “at the direction” of the candidate bolsters the evidence that the McDougal and Daniels payments were not just run-of-the-mill behavior.

Given that Cohen indicated that the payments were meant to influence the election and that they came at the direction of Trump, Lawrence Noble, former general counsel for the Federal Election Commission, told The Post, “there is little question Cohen, the campaign and the candidate are liable for the campaign finance violations.”

Noble outlined a slew of violations implied by the new filing: contributions in the name of another, failure to report the contributions, soliciting the illegal contributions, excessive contributions, illegal corporate contributions and acceptance of illegal contributions. These charges may involve civil or criminal penalties, depending on context, and would often focus on the campaign treasurer. But this case is exceptional.

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“In this case, you’re dealing with a situation where his lawyer who actually admits to doing the transactions says that they broke the law and that Trump knew about it,” Noble said. “This is something that very clearly would have to be considered for criminal prosecution” of Trump — were he not president. Department of Justice guidelines indicate that a sitting president cannot be indicted.

For Trump to be charged — if he weren’t president — it would need to be a “knowing and willful violation,” Noble said. This doesn’t mean, though, that Trump would need to know the specific statutes that his actions were violating. It would be enough for Trump to know that campaign contributions needed to be reported and were subject to limits, which he clearly did, and that the payments were being made to influence the election.

That Cohen and Trump went to great pains to obscure the payments bolsters the latter point. (Cohen “arranged one of the payments through a media company and disguised it as a services contract, and executed the second non-disclosure agreement with aliases and routed the six-figure payment through a shell corporation,” the filing reads.) In that leaked recording from earlier this year, Trump mentions a payment in cash, which would shield the payment from scrutiny. (His legal team insisted he was saying not to make the payment in cash.)

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“What’s unusual is you have the person who was the key operator in this” — Cohen — “did it for the purpose of influencing the election, and that the candidate knew about it," Noble said.

That sets this case apart from the case of former North Carolina senator John Edwards, who faced criminal charges for accepting contributions aimed at helping him hide a romantic relationship. In that case, there was no equivalent to Cohen implicating Edwards. (That relationship was brought to light, ironically, by the National Enquirer.)

In that case, Edwards was found not guilty on one count and other charges were eventually dropped. Rick Hasen, professor of law and political science at University of California at Irvine, warned that criminal charges would be similarly tricky to prove without a doubt, regardless of Cohen’s involvement.

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“Cohen’s pleading guilty to campaign finance crimes does not make Trump automatically guilty as well,” Hasen said. “If it ever came to a trial, Trump could claim he intended to keep the payments to mistresses secret for personal, not campaign, reasons, and it would be up to a jury to determine the credibility of such an argument.”

The government cited Cohen’s attempts to hide these payments in its call for a stiff prison sentence.

“Our system of voluntary compliance would be undermined,” the filing reads, “if wealthy and successful individuals such as Cohen come to believe that the most severe sanctions that they will face, in the relatively unlikely case that they are caught cheating on their taxes, are the payment of back taxes, interest, and penalties.”