Pinned to the top of Elon Musk’s X account is a six-minute clip of his recent three-hour interview with the podcaster Joe Rogan.

Although federal officials have long recognized improper spending as a problem, it is not the main reason for the program’s dire financial outlook

The involvement of Antonio Gracias, an investor who has known Elon Musk for two decades, suggests that Mr. Musk has made overhauling the Social Security Administration a priority.