WASHINGTON — Before Justice Brett M. Kavanaugh joined the Supreme Court, he served on a federal appeals court for more than a decade. In a memorable 2013 dissent, he reflected on the obligations of lower courts in the judicial hierarchy.

“It is essential that we follow both the words and the music of Supreme Court opinions,” he wrote, meaning that judges on lower courts must follow not only the letter but also the logic of Supreme Court precedents.

The Georgia Supreme Court took a different approach in a recent death penalty case, as a candid concurring opinion acknowledged. “The reasoning of the United States Supreme Court’s decisions does not bind lower courts,” Justice David E. Nahmias wrote in June, speaking for three members of his court. “Only the holdings govern.”

This was particularly true, he wrote, in cases concerning the Eighth Amendment, which bars cruel and unusual punishment. Whether given punishments are constitutional, the Supreme Court has said, must be judged against “the evolving standards of decency that mark the progress of a maturing society.”

When “it all comes down to whether five justices decide to ‘evolve’ the Eighth Amendment a little more,” Justice Nahmias wrote, “it is risky to rely on reasoning alone.”

The U.S. Supreme Court will soon decide whether to hear the case, which challenges a Georgia law that places an extraordinary burden on capital defendants seeking to be spared execution. In the process, the justices could clarify whether it is just the words or also the music of their precedents that binds lower courts.

The case concerns Rodney Young, who was convicted in 2012 of killing the son of his estranged girlfriend. Mr. Young grew up in New Jersey, where his schools classified him, in the language of the time, as “mentally retarded.” These days, they would call him intellectually disabled.

A 2002 Supreme Court decision, Atkins v. Virginia, ruled that the Eighth Amendment forbids putting intellectually disabled people to death. But the Georgia law at issue in the case, unique in the nation, requires capital defendants seeking to be spared execution to prove they are intellectually disabled beyond a reasonable doubt.

That is the standard that ordinarily applies to the government in criminal cases. It is intended to be hard to meet and, in the context of prosecutions, is meant to tolerate letting some guilty people go free rather than risk sending innocent ones to prison. The Georgia law inverts this dynamic, tolerating the executions of some intellectually disabled people.

Teachers and school staff members testified that Mr. Young satisfied the criteria for intellectual disability required by the Atkins decision. But the jury found that Mr. Young had not cleared the daunting hurdle of proving he was intellectually disabled beyond a reasonable doubt, and it sentenced him to death.

The Atkins decision largely let states decide who qualified as intellectually disabled. But two later decisions, in 2014 and 2017, struck down measures creating, as Justice Anthony M. Kennedy put it, “an unacceptable risk that persons with intellectual disability will be executed.”

The Georgia law has a curious origin story. Enacted in 1988, it was the first in the nation to ban the execution of intellectually disabled people, predating the Atkins decision by 14 years. But it was drafted in haste.

“I dropped the ball,” Jack Martin, one of the provision’s drafters, told the Georgia House of Representatives in 2013. He and his co-author, Mr. Martin said, had not meant to impose a reasonable doubt standard, but they put a key clause in the wrong place.

“It was sloppy draftsmanship, pure and simple,” Mr. Martin said. “I don’t think anybody intended that to happen.”

Almost every other state requires defendants to prove they are intellectually disabled by just a preponderance of the evidence — that is, by showing it to be more likely than not.

The difference in the two standards matters, lawyers with the American Civil Liberties Union, which represents Mr. Young, told the Supreme Court in a recent petition asking the justices to hear his case.

“In the states that apply a preponderance-of-the-evidence standard, approximately one-third of those asserting that they are intellectually disabled succeed in invoking the Eighth Amendment’s protection,” they wrote. “In Georgia, not a single person convicted of intentional murder has prevailed at trial in establishing that he is intellectually disabled.”

Comparing Georgia’s approach to that of other states only begins to suggest how unusual the law is, Mr. Young’s lawyers told the U.S. Supreme Court.

“As far as petitioner can tell,” they wrote, “there are no other circumstances whatsoever where an individual asserting a violation of his constitutional rights must establish the underlying facts beyond a reasonable doubt. In all of constitutional law, Georgia stands alone.”

Dissenting from the Georgia Supreme Court’s decision upholding the state law, Justice Charles J. Bethel said simple logic demonstrated that the law created, in the words of the U.S. Supreme Court, “an unacceptable risk” that some intellectually disabled people would be executed.

In his concurring opinion, Justice Nahmias, who served as a law clerk to Justice Antonin Scalia and is now the chief justice of the Georgia Supreme Court, acknowledged that the question in the case was a close one and that the reasoning in U.S. Supreme Court precedents “certainly casts doubt on this state’s uniquely high standard of proof.”

Justice Nahmias added another consideration, one seemingly grounded in a realistic assessment of the U.S. Supreme Court’s new conservative supermajority.

“If I had to guess today,” he wrote, “I would say that it is likely that if the United States Supreme Court, as currently comprised, is called on to decide whether Georgia’s beyond-a-reasonable-doubt standard for proof of intellectual disability violates the Eighth Amendment, a majority of the justices would not extend the holdings” of the decisions in 2014 and 2017 “to strike down our state’s statute, notwithstanding the reasoning of the majority opinions in those two cases.”