Carolyn Durst, 62, a sweepstakes winner in the pie competition at the Kentucky State Fair, said, “I give pie crust demonstrations to my friends, and I tell them, No. 1, you’ve got to have White Lily flour.”

Ms. Badertscher said that the new White Lily is also made solely from soft red winter wheat. But there are many other variables, like the grind of the flour. The Knoxville plant has long claimed that White Lily is ground finer and sifted more times than any other flour on the market. All that work costs a bit more  at an Atlanta supermarket this month, five-pound bags of White Lily went for $2.99, more than Gold Medal, which sold for $2.79, or the store brand, $1.82, but far less than specialty and organic brands.

Then there is the matter of what part of the grain is used. Underneath the husk of a wheat kernel, a layer of bran encloses the germ and a white substance called endosperm. White Lily is a patent flour, meaning it uses only the heart of the endosperm, the purest part. With wheat prices more than double what they were last spring, some fans fear that selectivity may be compromised.

“At the turn of the century, the question was, how pure and white can you get it?” said Fran Churchill, a former White Lily plant operations manager. “For economy, millers have pushed closer and closer to the bran,” she said. “Everyone in the industry is getting as much flour out of that kernel right now as they can.”

Unlike most all-purpose flours, White Lily is bleached with chlorine, a process that not only whitens the flour but weakens the proteins. Chlorination alters the starch particles to make batters more viscous, and thus less likely to fall. It loosens the strict balance of starch, liquid, fat and sugar that baking requires to allow for higher proportions of sugar  thus, sweeter cakes.

The chlorine makes White Lily more like cake flour than other all-purpose flours. But there again is another subtle difference, Ms. Corriher said. While White Lily can be used in cakes, it is not bleached as much as cake flour, which gives White Lily a better, less acidic taste, Ms. Corriher said. Pastry flour is also made from soft wheat, but it is not chlorinated.

Image Credit... Erica Yoon for The New York Times

Milling experts said that in theory, it should be possible to replicate White Lily. “If the source of the wheat is the same, the mill itself won’t be that hard to duplicate,” Mr. Hoseney said. Ms. Corriher, on the other hand, was more skeptical that a process perfected over more than a century of milling and subjected to Knoxville’s intensive quality control could be easily replicated.