On August 22, the New Mexico Supreme Court heard Barrie v Duran, 33755. The Court then ruled that the Secretary of State was wrong to have kept Jon Barrie off the November ballot (as the Independent American Party nominee for U.S. Senate) on the grounds that he wasn’t a registered member of the party that nominated him at the time of the Governor’s Proclamation. Here is the two-page order.
As to the other issue in the case, whether Barrie had enough valid signatures, the court sent that back to the lower court to resolve, but also said perhaps the candidate and the Secretary of State themselves can come to an agreement on how many signatures are valid. See this news story. The decision is not yet posted to the Court’s web page.