"Further, the Affiant sayeth not" - what does this mean?

It shows up on affidavits, and as a rough translation means, I presume, "beyond this, I (the Affiant) aren't stating anything futher" but it seems to be a stock phrase as if it's some magical amulet that protects the affiant from something, but I haven't figured out what that is. Can someone whose been through law school clarify this for me?

An affidavit is a sworn statement. The limitations of the sworn statement is within the document. Since it's sworn, any intentionally incorrect statements could result in perjury. "Further Affiant sayeth not" is archaic and a phrase I don't use, but it is common. It means--"these facts are the limit to the facts I will swear to." It protects the affiant from perjury.
The statement "Further, the Affiant sayeth not" is legalese. Translated into plain English, it simply means

"Th-th-th-th-that's all, folks!"

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