WASHINGTON >> It is one of the iconic moments in modern economics: A young professor named Arthur Laffer sketched a curve on a bar napkin in 1974 to show an aide to President Gerald R. Ford why the federal government should cut taxes.

The Laffer Curve became famous; the Republican Party became the party of tax cuts; and, in 2015, the Smithsonian announced that it was putting the napkin on display.

But the napkin now celebrated for starting a tax revolt is not, in fact, the original napkin, according to the people who were at the fabled meeting at what was then the Two Continents restaurant in Washington. In an interview this week, Laffer said it was most likely a keepsake created a few years later.

Among the clues: It is cloth, while the original napkin was paper. It is dated 9/13/74, while the original meeting took place after the November 1974 midterm elections. And it is inscribed to Donald H. Rumsfeld, then Ford’s chief of staff. Laffer met with Dick Cheney, Rumsfeld’s deputy.

Laffer said he did draw on the Smithsonian’s napkin, but he most likely did so several years later, at the request of journalist Jude Wanniski, who wanted a keepsake of the famous moment.

The napkin was found among Wanniski’s personal effects after his death in 2005. In a pair of interviews this week, Laffer said the Smithsonian did not contact him before putting the napkin on display, and that he learned about the exhibit only after the fact. He said he had never before been asked about the napkin’s authenticity.

“Look at how neatly it was done!” Laffer said of the museum napkin, on which he drew his curve, along with a brief explanation. “You tell me how, late at night with a glass of wine, you’re going to do it that neatly.”

Laffer’s Curve, which illustrates the theory that cutting tax rates can increase tax revenues, is enjoying a revival. The idea played a starring role in Republican campaigns for tax cuts in 1981 under President Ronald Reagan and in 2001 under President George W. Bush. Now Republicans are once again leaning on the Laffer Curve to argue that cutting tax rates would not increase the federal debt.

Speaker Paul D. Ryan, R-Wis., who has invoked Laffer’s theory during the current debate, keeps on the wall of his personal office a framed napkin illustrated and signed by Laffer and inscribed “to my friend, Paul Ryan.”

The Smithsonian presents its napkin as the tablecloth that started this tax revolt.

“Economist Art Laffer sketched a new direction for the Republican Party on this napkin,” the display says, “illustrating his theory that lowering taxes increased economic activity.”

Brian Domitrovic, a historian at Sam Houston State University who has studied and written about the creation of the Laffer Curve, said the sum of the available evidence shows that the Smithsonian’s napkin is “most certainly an ex post facto creation.”

But Peter Liebhold, the curator for the Smithsonian’s division of work and industry, who acquired the napkin in 2013, said that the museum was confident of its authenticity.

“As you know, oral history is wonderful but subject to problems,” he wrote in an email. “The Two Continents meeting happened many years ago, and some of the participants’ memories of details may be slightly off. In this case, we have a piece of primary material that clearly documents the occasion. I look forward to your story, but strongly stand by the authenticity of the Smithsonian artifact.”

The Laffer napkin has long been shrouded in mystery, partly because none of those present at the original meeting thought that it was particularly historic at the time.

Wanniski, the hype man of the tax cut movement, was the first to publish an account in 1978, which he embroidered in multiple retellings. He was working for The Wall Street Journal’s editorial page in 1974, and he said that after the Republicans suffered sweeping losses in the 1974 midterm elections, he arranged a meeting between Laffer, whose ideas he considered important, and Cheney.

The economy was mired in stagflation, the unfortunate combination of high inflation and high unemployment. Laffer, then a professor at the University of Chicago, was a leading spokesman for a new school of economic thought, supply-side economics, that saw tax cuts as the best way to increase economic growth while reducing inflation.

The two men met for drinks with Wanniski in early December at a restaurant across the street from the Treasury Department. Wanniski also invited Grace-Marie Arnett, a Republican aide who was interested in supply-side economics.

In Wanniski’s account, Laffer grew frustrated as he tried to explain the value of tax cuts to Cheney, finally grabbing a paper napkin so he could draw a visual aid. The Laffer Curve, which looks like the nose of an airplane, is meant to show that higher tax rates can reduce tax revenues — and lower tax rates can bring in more money.

Arnett, now known as Grace-Marie Turner, said that she recalled the moment vividly because she had never seen the Laffer Curve before, and she found it illuminating.

She said she was certain that the meeting happened after the elections because until then, she was working for a Republican House candidate in Texas. And, she added, “I absolutely know that it was a paper cocktail napkin.”

Cheney also wrote in his memoirs that the meeting happened after the midterms.

Laffer has always said he does not have a clear recollection of the original meeting, but he said that he does not regard the Smithsonian’s napkin as the authentic original.

“There was a napkin done, and I don’t know where it ended; I guess it was probably in the trash,” he said. “And Jude Wanniski wanted me to do another example of it two years later, and I believe that this is the napkin that Jude Wanniski asked me to do for him.”

Wanniski never mentioned the cloth napkin in his public writings. In June 2005, shortly before his death, he published an account of the original meeting on his website. He wrote again that Laffer drew the curve on a cocktail napkin, in December 1974, and he specifically denied that Rumsfeld was there.

Patricia Koyce Wanniski, his widow, said in an interview that she found the napkin at the back of a drawer of Wanniski’s clothing after his death.

Why did Laffer dedicate the napkin to Rumsfeld and write the date “9/13/74”?

One possible explanation is suggested by Rumsfeld’s 2011 memoir. He wrote that his datebook showed he had dined with Laffer and Cheney on Sept. 16, 1975, and that he had made a note at the time that Laffer drew a curve on a napkin.

Is it possible Laffer reprised that napkin for Wanniski, creating a reproduction of a reproduction? Laffer said he simply was not sure.

“When you get old,” he said, “it’s hard to say which napkin was which and when and where.”