On Friday, July 14, U.S. District Court Judge David Nuffer held a hearing in United Utah Party v Cox, 2:17cv-655. It lasted three hours and seemed to go well for the party, which wants its nominee on the November 2017 ballot for the special U.S. House election, 3rd district. A decision is expected next week.
UPDATE: here is a news story about the hearing. FURTHER UPDATE: here is the Associated Press story.
Here is the Salt Lake Tribune story.