As technology advances, the art world has turned to microscopic analysis and pigment testing to buttress — or challenge — the judgments of a tiny club of experts whose opinions have long been treated as law. This pursuit of scientific validation has only deepened as art historians and institutions like the Pollock-Krasner Foundation, which shut down its authentication board in 1996, retreat from certifying art for fear of being sued.

But science has its limits. Paint or paper may help establish the date of a work, while hair and fibers can help pinpoint where it was made. A work’s provenance must also be verified. Still, connoisseurs — as well as most auction houses who rely on them — maintain that true authorship cannot be established without an expert evaluation of the composition and individual strokes that reveal an artist’s “signature.”

In this case, the difference of opinion could be worth millions. Unauthenticated, “Red, Black and Silver” would be listed as “attributed to Pollock” and carry an estimate of no more than $50,000, said Patricia G. Hambrecht, chief business development officer at Phillips auction house, where the painting is consigned. If judged a Pollock, the painting’s estimated value would soar to seven figures, she said.

Ms. Kligman’s account of the painting dates to the summer of 1956 when she was 26 and living in Pollock’s house in East Hampton, N.Y., after Krasner, having caught the lovers together, sailed for Europe. Pollock was in an alcoholic tailspin and hadn’t painted in two years. As Ms. Kligman detailed in a new introduction to the 1999 edition of her memoir, “Love Affair: A Memoir of Jackson Pollock,” the artist was on the lawn when she brought him his paint and the sticks he used. After he finished, he said, “Here’s your painting, your very own Pollock.”