The FAA seems not to use the C/N term.
https://www.faa.gov/licenses_certifi...dia/ardata.pdf
I have not found an example of an American manufacturer using the term C/N
You've created confusion now
Fris. The P-51 book I took the info above from uses the term C/N and is written by an American resident. The question now is his use of C/N legitimate? It was designed and built to a British requirement so perhaps they, North American, adopted the British convention.
It does seem that the term C/N has entered wide use today irrespective of the aircrafts source.
https://aviation-edge.com/database-c...mber-aircraft/