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early 14c., "person or thing that clinches" (i.e., secures nails by bending down or riveting the pointed end), late 15c. as a class of shipyard worker; agent noun from clinch (v.). As a type of nail, from 1735; as a conclusive statement, argument, etc., 1737.
The deciding or conclusive element; the BOTTOM LINE: One smudged fingerprint was the clincher (1830s+)