Any communications he had with the White House about the testimony would have been important only insofar as there was a discussion of its content. The president would have had a keen interest. It is exceedingly unlikely that he did not know what members of his staff and his lawyers learned about what Mr. Cohen was prepared to say. We also know that Mr. Cohen lied about the Moscow hotel project.

While in his plea agreement Mr. Cohen noted that he understood and sought with his lies to bolster one aspect of the president’s public messaging on Russia — namely, that he had no business dealings with the Putin government — he did not say anything inconsistent with the possibility that the president knew that Mr. Cohen planned to lie to Congress. Did Mr. Trump encourage Mr. Cohen directly, or through others, to lie about the hotel project, to protect his public account? Or did the president, knowing Mr. Cohen would tell a lie, acquiesce in the false testimony — signaling with this silence approval, or at least acceptance?

A similar question is presented in the case of Paul Manafort. The memorandum filed by prosecutors set out Mr. Manafort’s breach of his cooperation agreement. Contrary to his express representations to the government, he was in contact with the White House, with a “senior administration official,” in 2018. The prosecutors make clear that they have evidence of multiple contacts. Who was Mr. Manafort communicating with, and about what? That he was bidding for a pardon is one possibility. Another is that he was making sure that the president knew that he was holding the line — against telling the truth about the matters under investigation.

In the same week we learned that Michael Flynn, unlike Mr. Cohen and Mr. Manafort, was actively cooperating. It’s not yet in the public record, but one issue on which he is certain to have come clean are the circumstances in which he lied to the F.B.I. about discussions in December 2016 with the Russian ambassador. It is known that Sally Yates, then the deputy attorney general, briefed the White House counsel promptly about the problem with Mr. Flynn’s F.B.I. interview, and Mr. Trump’s press secretary later assured reporters that the president was immediately briefed about “the situation.”

Yet weeks passed before the president fired Mr. Flynn, and when he did he did so, he cited lies told to the vice president, not investigators. In other words, Mr. Trump steered clear of holding Mr. Flynn responsible for the criminal offense. Mr. Flynn may have light to shed on the president’s motives for this reticence. Mr. Trump might have avoided addressing publicly the lie to the F.B.I. if he had any part in it — either by encouraging Mr. Flynn to lie, or because he has been willing to wait out the “situation” and see if Mr. Flynn could get away with it.