Jason Strauch v. New Mexico

Was the New Mexico Supreme Court's denial of Mr. Strauch's State Writ ofMandamus, contrary to the United State Constitution First Amendment, Right to Redress Grievances, and Fourteenth Amendment Due Process and Equal Protection of the Law clause, pursuant to US Supreme Court Rule 10(c)? The Writ of Mandamus was filed to compel the New Mexico's Second Judicial District Court to obey New Mexico legislated Statutes and Constitution mandating the right to file appeals.*

Has the New Mexico Second Judicial District Court violated the Fourteenth Amendment Due Process and Equal Protection of the Law clause by refusing to abide by the governing New Mexico Statutes and New Mexico's Constitutional right to file an appeal, pursuant to US Supreme Court Rule 10(c)?