Before we dig into Monday’s Supreme Court oral arguments, a quick pop quiz: What percentage of criminal cases in the United States are resolved through actual trials, with testimony and evidence and cross-examination and a final verdict rendered by a judge or jury?

If you answered anything more than 5 percent, you’ve failed the quiz. As much as America loves to brag about its preservation of jury trials as the centerpiece of our criminal justice system, hardly anybody has them anymore. Instead, for better or for worse—OK, definitely for worse—about 95 percent of defendants work out a plea bargain with the prosecutor, typically admitting their guilt in exchange for reduced charges. Then the defendant attends a sentencing hearing, where the prosecutor makes her recommendation, and the judge must decide the appropriate punishment. That hearing is often the only “trial” the defendant will receive.

Plea bargaining is terrible for a bunch of reasons, not least of all because it often compels innocent people to plead guilty. But Monday’s case, Betterman v. Montana, is not strictly about the evils of plea bargaining. Rather, it poses a seemingly simple question: Once a defendant has accepted a plea deal, can the government detain him for 14 months before giving him a sentencing hearing?

You might respond to this question by reciting the Sixth Amendment, which states that “In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial.” Even by the measure of our perpetually clogged-up court system, 14 months is not “speedy,” and so Brandon Thomas Betterman—the defendant here who spent all that time waiting for a hearing—should win. But Montana disagrees, insisting that Betterman’s right to a speedy trial was never violated. That’s because, in Montana’s telling, a sentencing hearing isn’t a trial at all, and so isn’t subject to the Sixth Amendment’s speedy-trial guarantee.

There are two problems with that argument, not including the fact that it would upend 50 years of precedent. The first was highlighted repeatedly throughout the morning by Justice Elena Kagan, whose vim is invigorating on an otherwise torpid court. (I counted at least four catnaps by three justices over the course of the hour.) A delay in court proceedings, Kagan noted, may “impair the defense”: Evidence disappears; witnesses scamper off; memories fade. This problem is present in both conventional trials and sentencing hearings.

“You know,” Kagan tells Montana Solicitor General Dale Schowengerdt, “in most cases these days, most of the actual adjudication of contested issues goes on in sentencing rather than at the trial stage, given that we don’t have very many trials anymore.”

Schowengerdt, who previously spent his days defending businesses’ right to discriminate against same-sex couples, is unfazed. He suggests that sentencing hearings don’t really involve the kind of factual disputes that missing evidence could affect. Kagan pushes back.

“There may also be real factual disputes!” Kagan says. “It might be about the amount of loss. It might be about the amount of drug quantity. It might be about prior bad acts. It might be about a whole range of things which are the kinds of things that we actually typically think of as contested issues at trial.”

Kagan is trying to demonstrate why it’s logical to treat sentencing hearings as part of the trial for Sixth Amendment purposes. Schowengerdt pushes back, asserting that the point of the Speedy Trial Clause is to try potentially innocent people quickly so they aren’t forced to languish in jail if they haven’t committed a crime. But Schowengerdt’s claim—that the clause was designed to protect innocent people—doesn’t hold up to scrutiny.

“A very significant part of this rule has to do with impairment of the ability to defend yourself,” Kagan reminds Schowengerdt. And “that kind of consideration applies just as well at the sentencing phase as it does at the conviction stage—maybe in most cases more so, given that most of the action these days takes place at the sentencing phase.”

But Kagan’s questions register as irrelevant to Schowengerdt, for a pretty troubling reason: He argues that guilty people don’t deserve a speedy sentencing hearing because they are guilty. Under Schowengerdt’s theory, when a defendant has pleaded guilty, he has extinguished his speedy-trial right. Never mind that this conception of the Sixth Amendment would nullify its centerpiece for 95 percent of defendants, or that as many as 8 percent of people who plead guilty are innocent. Once you take a plea deal, your speedy-trial right is toast.

If sentencing hearings were historically separate from trials, a low-key epilogue to the main event, Schowengerdt would have a point. But that brings us to the second problem with his argument: It is a brazen twistification of the historical record. As the Supreme Court recognized in the 2000 ruling Apprendi v. New Jersey, there was no meaningful distinction between a trial and a sentencing hearing when the Sixth Amendment was ratified. In fact, they weren’t even seen as separate trials, but rather as the guilt-determination and sentencing phases of the same trial. Only in modern times have we routinely separated the two proceedings. Thus, the framers would be puzzled by the question of whether “the right to a speedy trial” encompasses the right to a speedy sentencing. Of course it should encompass both—at the founding, there was no difference between the two.

Now I have to tell you a very sad truth, which is that Justice Samuel Alito only accepts the reality of American legal history when it aligns with his judicial ideology. Shocking, I know, but it helps to explain why Alito jumps down the throat of Fred A. Rowley, Betterman’s excellent attorney.

“At the time of the adoption of the Sixth Amendment, weren’t post-trial but pre-sentencing delays fairly common?” Alito asks Rowley.

Not quite, Rowley explains patiently. “As a general rule, the sentencing did take place soon after the jury issued its verdict, and oftentimes immediately.”

Rowley’s assertion here is backed up by a long line of post-Apprendi cases citing a vast historical record which proves that, from the early days of the republic, sentencing promptly followed a guilty conviction. But Alito thinks all that evidence is “dubious,” and on Monday, he tells Rowley it is “just not true as a historical matter.”

Looking more confused than flustered, Rowley begins to recite the historical record affirmed in Apprendi. Alito, even more visibly nettled than usual, cuts him off.

“That just isn’t true,” he repeats. “We don’t have the right to change history. It isn’t true.”

This retort presents an interesting practice question: What should an oral advocate do when a Supreme Court justice denies reality? Luckily for Rowley, the clock is on his side, and time runs out before Alito completes his metamorphosis into a Senate Republican.

By the time the hour is up, it’s unclear whether Betterman has any prospects for relief. He argues that his sentence should be reduced by the number of months for which he was detained unreasonably without a hearing—a pretty reasonable solution. But if the court splits 4-4, he’s out of luck, because the Montana Supreme Court rejected his constitutional claim. There’s reason to think that won’t happen; Justice Anthony Kennedy is wary of plea bargaining, and Justice Clarence Thomas is skeptical of constitutional rules that distinguish between conviction and sentencing. It would be nice to see a diverse coalition of justices affirm the continued vitality of the Sixth Amendment in our plea-bargain world. But even if that happens, it seems that we can be sure that Alito will pen an incensed dissent, confronting a barrage of facts and history and shouting not true, not true, not true.