A writ of coram nobis is a request to a judge to reopen and reconsider a matter that has already been decided. The basis for the request is a claim that the decision is based on a mistake of fact, which can now be rectified.
Judiciary Act, Sec. 81-82. See United States v. Morgan, 346 U.S. 502 (1954), holding that the All Writs section of the Judicial Code, 28 U.S.C. Sec. 1651(a), gives federal courts the power to employ the ancient writ of coram nobis.
Pursuant to the Presentment Clause, a Congressional Act is signed into law by the President and then transferred to the Archivist of the US as evidence of US law. All evidence of US law is held in trust by the Archivist of the United States. The Archivist is appointed by the President. An ineligible President invalidates appointments made pursuant to the Appointments Clause. Evidence of law held in trust by an Archivist appointed by an ineligible President puts the Judiciary Act, as amended, in jeopardy.
The Judiciary Act provides authority for the District Court to operate. The Act established a circuit court and the district courts in each judicial district. An ineligible President voids the authority of the district court and ultimately the U.S. Constitution. The courts are avoiding eligibility challenges to preserve the status quo with disregard for their oaths to support the U.S. Constitution pursuant to Article VI.