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Are there a certain set of numbers that if they match are "matching numbers"? Also, I have seen reference to an acronym of NOS. What does that mean?
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The meaning of "matching numbers" depends on how intent you are on meeting the strict judging standards of the major Corvette organizations, like the NCRS. In it's most basic form, it means that the partial vehicle serial number stamped on an engine pad (that extends forward from under the front of the passenger-side head) matches similar stampings on the frame (atop the left frame rail in the vicinity of the shock mount on a C2) and the serial on a small alumninum plate affixed under the passenger dash. Each of the numbers in those 3 places will always contain, in series, the last 5 digits of the vehicle serial number, although other parts of those stamped numbers may vary.
A strict interpretation also means that those numbers are not forged (ie, no cheating allowed), but that these parts (engine, frame, body) are the self-same actual parts the car had when it left the factory. For judging, many more numbers and markings are checked for being exactly like ("matching") the parts that would have been on the car when it was built, including casting numbers, dates, etchings, finishes, etc, etc. This would include things like bellhousing, heads, manifolds, distributor, tranny & differential, window glass, alternator, water pump, radiator, etc, etc, etc... ad infinitum.
"NOS" is often misused... it means "new old stock", which refers only to unused original Chevrolet parts that have been sitting on a shelf somewhere these many years. Unfortunately, sellers often use the term (knowingly or mistakenly) for used original parts, or for replacement parts from other makers (or even from Chevrolet) when the part is not precisely identical to the original.
