A basic tenet of a constitutional republic is that all law is authenicated, published and archived. The federal courts are authorized to accept copies of the originals if a reasonable assurance can be made the originals are archived and maintained by a President and his officers who are not in violation of the US Constitution. Evidence must be preserved and protected by individuals authorized by the Constitution or the evidence is tainted.
The President is the Chief Executive Officer of the US federal government. An ineligible President voids the Constitution and all US law, rules, regulations, treaties and executive orders because the chain of custody of preserving and protecting the evidence of US law is destroyed.
There are many reasons the Constitution requires an eligiible President at all times. One of those reasons is to maintain the chain of custody of US law as evidence of law in the archives. Only an eligible President can appoint or delegate authority to the Archivist of the United States.
Interpretations of legalistic esoterica like “chain of custody” are not what makes the governing document valid or invalid.
Ultimately it is the willing compliance of the bulk of the legitimate electorate (as distinct from the general population) that makes The Constitution the Law of the Land.
Just as that Constitution is currently being ignored, vilified and trampled by lawless usurpers, it can be reenforced by a simple show of will by the electorate or (in an extreme case) by the forcible removal of the offending traitors.
Either way, it is the de facto allegiance that the document is given which establishes its de jure validity.
The 10th Amendment is a perfect case in point. It has long been held in de facto contempt by the Federal Government and the passive acquiescence of the States. For this Amendment to have any validity outside of being a de jure oddity, it will take concrete action and defiance - to the point of armed resistance - on the part of the States. In fact this is why the 2nd Amendment calls on every citizen to be armed as a potential militiaman for his respective State.
A large part of the genius behind the Bill of Rights is that the various parts serve to support one another, this being an optimal example.