After nine years of legal wrangling, the relationship between American commerce and cats — cats of the six-toed variety — has been decided.

A U.S. Court of Appeals panel ruled that certain polydactyl felines said to have an ancestral association with a famous writer “substantially affects interstate commerce.”

This is exactly why we need judges who can see beyond the obvious.

Me? I’ve visited Ernest Hemingway’s Home and Museum in Key West and utterly missed the legal and commercial significance of self-satisfied kitties slouching through the house and garden more like aristocrats than cats.

These furry scofflaws lazed around as if they were beyond the reach of federal regulators.

Since 2003, the U.S. Department of Agriculture has gone after the museum and its free-ranging cats with the fervor of Javert in pursuit of Jean Valjean. The USDA decided a 1966 federal law meant to curb the shabby treatment of animals confined in low-rent zoos and traveling carnivals applied to a herd of six-toed house cats roaming the grounds at 907 Whitehead St.

At one point in this long, mad struggle, the USDA demanded cages, electric fences, a night watchman. All the rules that might apply to a ferocious zoo animal.

The agency sent in undercover investigators, who stuffed the court records with surreptitious photos of six-toed cats, including a snapshot of a suspicious-looking gray cat with the caption: “Picture of six-toed cat taken in restaurant/bar at end of Whalton Lane and Duval. May or may not be a Hemingway Home and Museum cat.”

Experts were hired. They invariably decided the kitties were kept in healthy, comfy luxury, but the USDA still figured some obscure legal principle was at stake. The feds muttered that they might seize the cats.

The three-judge appeals panel that decided this case last month was not unsympathetic to the Hemingway museum’s contention that it’s not actually in the zoo business. “We appreciate the Museum’s somewhat unique situation, and we sympathize with its frustration.”

But the museum displays photos of cats, all said to be descendants of Hemingway’s six-toed cat Snowball, in brochures and on the museum’s website. Apparently that amounts to interstate commerce.

So the USDA won jurisdiction over Ernie’s cats. (Not that this will likely affect the 45 creatures. Back in 2008, the museum agreed to tighten up cat security and other concessions while the case wended its way through the courts.)

Meanwhile, the same agency that spent so much time and money on behalf of the most pampered cats in South Florida has shrugged off the hideous cruelties of factory farming — chickens, pigs, cows stuffed with hormones and confined for their entire wretched lives in tiny pens.

Nor have USDA investigators reacted to revelations that the thoroughbred racing industry was stoking horses with so many painkillers and performance-enhancing drugs that 3,000 animals a year sustain fatal racing injuries.

Apparently, industry fat cats enjoy a bit more deference than Key West polydactyls.