WASHINGTON — Supreme Court opinions have come down with a bad case of link rot. According to a new study, 49 percent of the hyperlinks in Supreme Court decisions no longer work.

This can sometimes be amusing. A link in a 2011 Supreme Court opinion about violent video games by Justice Samuel A. Alito Jr. now leads to a mischievous error message.

“Aren’t you glad you didn’t cite to this Web page?” it asks. “If you had, like Justice Alito did, the original content would have long since disappeared and someone else might have come along and purchased the domain in order to make a comment about the transience of linked information in the Internet age.”

The prankster has a point. The modern Supreme Court opinion is increasingly built on sand.

Hyperlinks are a huge and welcome convenience, of course, said Jonathan Zittrain, who teaches law and computer science at Harvard and who prepared the study with Kendra Albert, a law student there. “Things are readily accessible,” he said, “until they aren’t.”