James Barron got to within inches of the world’s most sought-after stamp: a $9.48 million, mutely colored, octagon scrap that dates back to 1856. He gained proximity two years ago, when this postmarked treasure, known as the One-Cent Magenta, was due to be measured and photographed at the Smithsonian Institute.

Recently recounting the experience, Barron, a reporter, makes the Magenta sound as alluring as a reclusive, wildly desired, relic of a supermodel from the swinging ’60s.

“I got to breathe on the stamp,” he says. “There are people from the world of stamps who say that my DNA is now on it.”

Barron, 61, remembers the encounter taking place on a sunny day in DC. He recalls that gorgeous natural light flooded a workroom where the Magenta was being measured with a spectrometer. The stamp, having spent decades locked in a vault, had been carefully removed from its plastic carrier. Tweezers held it so that no oil-bearing flesh touched its fragile edges.

“I was as close to it as I could be,” says Barron. “The experience was a thrill, considering where the stamp had been over the years.”

The collectible’s unlikely odyssey is laid out in Barron’s new book, “The One-Cent Magenta: Inside the Quest to Own the Most Valuable Stamp in the World” (Algonquin Books of Chapel Hill), out Tuesday. Barron tells the tale of a coveted stamp that was uncovered inside a house in Guyana (then called British Guiana) and went through nine owners — such as a pioneering philatelist, an Austrian prince, a hot-headed widow and a consortium of investors — including the current one: ladies’ shoe mogul Stuart Weitzman.

Like all owners of the rather homely Magenta, Weitzman has his own, particular reasons for possessing it. The stamp is believed to be one of a kind. In a possibly apocryphal story, Arthur Hind, a self-absorbed industrialist who bought it in 1922 for $32,500, was approached by a collector who supposedly had a second One-Cent Magenta. The tale goes that Hind bought the duplicate stamp for “a big sum” and promptly incinerated it with the hot tip of his cigar, thus ensuring his object’s uniqueness — which is the sort of thing Weitzman goes after as a collector and investor.

“I think it is very value-oriented,” says Barron. “For Weitzman, one-of-a-kind is what matters in what he collects.” To wit, the designer has a shoe signed by the 1941 Yankees and, adds Barron, “There was a flag he tried to get because it was one-of-a-kind.”

For previous owner, John E. du Pont — the late, homicidal, eccentric heir played by Steve Carell in “Foxcatcher” — the One-Cent Magenta held a different sort of allure.

“Du Pont, [a serious stamp collector], wanted it because it would allow him to put together a complete collection of Guianan stamps,” Barron says. “He beat out four other bidders [at a 1980 auction] for the stamp. One of the people who worked with du Pont told me that he always bought the best; the One-Cent is up there.”

Though du Pont paid $935,000 for the rarity — and would try, unsuccessfully, to use the exhibition of it as leverage in negotiating the discharge of his prison sentence for the murder of wrestler Dave Schultz — du Pont did not exactly treat it like a prize. As related in Barron’s book, he once dropped the stamp on the floor and broke with philatelist protocol by casually picking it up with his fingers and risking a smudge. Collectors who saw it “were appalled, just as others were by Hind sticking tape on the backs of valuable stamps.”

Maybe, in their own blundering ways, du Pont and Hind were paying tribute to the fact that this stamp should have never existed in the first place.

It was created in the wake of a stamp shortage in British Guiana, produced on the fly, with no forethought to design or aesthetics, and used to cover postage on the mailing of a weekly newspaper. Barron estimates that some 500 of the 1-cent stamps were printed and almost all thrown away with that edition of the paper.

Then, in 1873, it happened to be found by a 12-year-old boy named Louis Vernon Vaughn who had been charged with cleaning out his uncle’s home.

“It only survived because, for some reason, Louie’s uncle saved that issue of the newspaper,” says Barron. “Louie found it and happened to be in this newfangled hobby of stamp collecting.”

He extracted the postage from the paper, sold it for 6 shillings — $16.83 in today’s currency — and initiated what one expert calls “the worst stamp swap in history.” Barron recounts a Vaughn family member telling him, “This is the one that got away.”

Of course, nobody could have guessed that a less-than-spectacular looking stamp would so seize the imagination of wealthy and powerful collectors.

“The One-Cent Magenta is hard to fall in love with,” Barron says. “I did not fall in love with it instantly, but it is not ugly. This was a fast and dirty solution. The stamp was not meant to last 160 years. And that is part of the beauty.”