1 a solemn promise, often invoking a divine witness, regarding one's future action or behavior : they took an oath of allegiance to the king.
• a sworn declaration that one will tell the truth, esp. in a court of law.
So one reason would be a solemn promise invoking a divine witness and the other is a sworn declaration to tell the truth in a court of law.
To perjure is willfully tell an untruth when giving evidence to a court; commit perjury.
These Article VI named officials are not in a court of law therefore cannot be held to perjury.
Their oath or solemn promise is made to what is a label namely, "The Constitution of the United States" which is not a document because there is no evidence the this label is a documnet. There would only be evidence that this label is a document if the document was signed by the one which takes the oath.
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