Last week, federal prosecutors in Washington and New York filed sentencing memorandums with federal judges in advance of the sentencings of Paul Manafort and Michael Cohen. President Donald Trump's former campaign manager and his former personal lawyer had pleaded guilty to federal crimes, and the memorandums, which are required by the federal rules of criminal procedure, set forth the prosecutors' desired prison sentences for them.

Judges rely on these submissions, as well as on those of defense counsel, before making the mathematical calculations that the law requires. Sadly, sentencing today is largely an algorithmic function, dictated by federal sentencing guidelines, with some room for judicial deviation based on the facts of the crimes and the personal backgrounds of the defendants. In my career as a judge in New Jersey, I sentenced more than 1,000 people using state guidelines that were substantially similar to the present federal guidelines.

When the federal prosecutors made their submissions for the most part public, they revealed two disturbing facts. Special counsel Robert Mueller in Washington revealed that in the government's view, Manafort had reneged on his plea agreement by lying to FBI agents who were sent to debrief him about his contacts with the White House. And federal prosecutors in the U.S. District Court for the Southern District of New York revealed that some of Cohen's crimes had been committed with the knowledge of and at the direction of Trump or to shield him.

Then all hell broke loose. Here is the back story.

Manafort, who has been convicted of federal financial crimes in Virginia, opted to avoid a second trial in Washington, D.C., on another set of alleged federal crimes by pleading guilty and agreeing to cooperate with the special counsel's office by truthfully telling its FBI agents what they sought to learn about ongoing investigations of President Trump.

The FBI agents wanted to know whether Manafort knew whether Trump committed any federal crimes -- such as conspiracy (namely, agreeing to receive foreign assistance during his campaign), obstruction of justice (interfering with the FBI in order to keep it from investigating him) and bank and tax fraud before he was president.

When the special counsel announced that Manafort had declined to be truthful to its FBI agents and Manafort's lawyers claimed he had been truthful, that conflict set up a dispute that must be resolved by a federal judge -- after a public hearing -- before she can sentence Manafort. That hearing will most likely reveal what prosecutors wanted to learn about Trump and what they claim Manafort lied about. Even though the hearing -- which has not been held as of this writing -- could be explosive about Trump, the president claimed he was exonerated by this turn of events.

At the same time, career prosecutors in New York -- whose chief, a Trump appointee, has removed himself from the case -- asked a federal judge to sentence Cohen to substantial prison time for the crimes to which he pleaded guilty, notwithstanding the substantial assistance he had provided them in their investigations of the president. Of the president? Yes. The feds in New York City, as well as the special counsel in Washington, are investigating the president? Yes.

How do we know this? We know that Cohen pleaded guilty to tax evasion, bank fraud, lying to Congress and campaign finance violations. According to the submission of the special counsel, Cohen lied to Congress -- about candidate Trump's efforts to build a hotel in Moscow by cutting a deal with Russian President Vladimir Putin during the presidential campaign -- to protect the president, who had publicly denied any campaign-time communications with Russians.

But the most damning thing we learned from the submission of the New York federal prosecutors was that they have evidence that Cohen's deceptive and criminal payments of hush money to women alleging to have experienced sexual intimacy with Trump before he was an active candidate were made "in coordination with and at the direction of" the president.

Prosecutors in the Southern District of New York enjoy the highest reputation for excellence in the legal, judicial and law enforcement communities. They know that they cannot ethically make a charge in federal court without corroborated evidence to support it. In their Cohen sentencing memorandum, they chose to reveal the existence, but not the substance, of their evidence against the president.

Think about the significance of this. The Department of Justice has accused President Trump of coordinating with, ordering and paying Cohen to commit a federal crime for which Cohen has pleaded guilty. Stated differently, career federal prosecutors who are not in the office of special counsel Mueller have told a federal judge that they have corroborated evidence that the president committed felonies.

Let's be clear. If A pays B to shoot someone and B does the shooting, A is as criminally liable as he would be if he had pulled the trigger.

Nevertheless, when the president learned of all this, the revelation of which had been authorized by his chosen but unconfirmed acting attorney general, he claimed that this submission, too, exonerated him. I was sorry to learn that.

These submissions place the president directly in the legal crosshairs of federal prosecutors -- closer to knowing about a campaign-time agreement for something of value with Russians than we have heretofore been. And they show a more direct procurer of criminal behavior than we have heretofore had.

The president may want the public to think that none of this troubles him. Yet the evidence of the falsity of his publicly denied proximity to Putin during the campaign and the possession of evidence by the Department of Justice of his pre-presidential criminal behavior are gravely serious, and he cannot reasonably pretend that they are not.

He can try to avoid reality, to paraphrase Ayn Rand, but he cannot avoid the consequences of avoiding reality. Those consequences may be fatal to his presidency and to his liberty.