Mr. Cohen testified there was “no doubt” that Mr. Trump knew what these payments were for, that candidate Trump directed him to “use my own personal funds from a home equity line of credit to avoid any money being traced back to him that could negatively impact his campaign.” The decision to pay Stephanie Clifford, known as Stormy Daniels, for her silence directly followed the revelation of an “Access Hollywood” video in which Mr. Trump claimed that he sexually assaulted women. Mr. Cohen testified that Mr. Trump decided to make the payment to Ms. Clifford because Mr. Trump worried that a second scandal would negatively affect his chances of winning the election.

The most compelling evidence produced by Mr. Cohen on Wednesday was not anything he said but two documents he produced: copies of two $35,000 checks he received in 2017, one signed by Allen Weisselberg, the chief financial officer of the Trump Organization, and Donald Trump Jr., the other by President Trump. With these and nine other payments over the course of that year, Mr. Cohen was “reimbursed” by the Trump Organization and President Trump for the money that Mr. Cohen spent to pay Ms. Clifford for her silence. The payments also included a $60,000 bonus for Mr. Cohen — presumably a reward for his loyalty.

These checks are key. They corroborate Mr. Cohen’s testimony and provide hard evidence that Mr. Trump and senior executives at the Trump Organization knew of and committed overt acts in furtherance of a conspiracy to violate campaign finance law and cover up those violations. Additionally, the checks are evidence that Mr. Trump knowingly made a false statement when he failed to report his liability to Mr. Cohen on his personal financial disclosure form in June 2017. This potential felony was committed while Mr. Trump was president.

Mr. Cohen explained he was confident that Mr. Trump would repay him the $131,000 that Mr. Cohen borrowed in his own name, quoting a conversation he had with Mr. Trump in the White House in February 2017. Mr. Cohen testified that President Trump said: “Don’t worry, Michael, your January and February reimbursement checks are coming. They were FedExed from New York and it takes a while for that to get through the White House system.”

Mr. Trump’s intent to influence the election by directing these contributions would be a crucial part of any potential prosecution for felony campaign finance violations. Mr. Cohen’s testimony is substantial, powerful evidence that President Trump understood he had a liability to Mr. Cohen from the beginning of his presidency and that Mr. Trump acted with the requisite intent to be subjected to prosecution for criminal campaign finance violations.