The Supreme Court on Monday struck down a North Carolina law barring convicted sex offenders from using popular social-media sites, including Facebook and Twitter. The justices unanimously ruled in favor of Lester Packingham Jr., who bragged online that he had beat a traffic ticket, leading to his conviction for violating a 2008 law intended to keep sex offenders away from social sites frequented by children. He was previously convicted of statutory rape. The state claimed the law holds the virtual world to the same standards as the real world: in which sex offenders are not allowed on playgrounds. Instead, wrote Justice Anthony Kennedy, the law was a violation of the First Amendment guarantee of free speech. “This case is one of the first this court has taken to address the relationship between the First Amendment and the modern Internet. As a result, the court must exercise extreme caution before suggesting that the First Amendment provides scant protection for access to vast networks in that medium,” Kennedy wrote.