Far-right conspiracy theorist Alex Jones has asked the U.S. Supreme Court to hear his appeal of the $1.4 billion judgment a Connecticut jury and judge issued against him for calling the 2012 Sandy Hook Elementary School shooting a hoax.

The Infowars host argues in a filing to the court that the judgment for defamation and infliction of emotional distress violates his constitutional rights, including freedom of speech and protections against excessive punishment.

The shooting killed 20 children and six adults in Newtown, Connecticut. The legal judgment came in lawsuits filed by some of the shooting victims’ relatives, whose lawyers dispute Jones’ claims to the Supreme Court.