Aircraft do not have a singular unique identifier that is time invariant.
While it is true that aircraft have serial numbers issued to their airframe, by itself, aircraft serial numbers are not unique.
The only unique identifier for an aircraft across its lifecycle from production to end of life is a combination of the manufacturer, make and serial number.
I know this because I am on (for better or worse) the patent that involves defining that as a unique identifier for aircraft.
The combination of ICAO aircraft type designator + serial number approximately is the most permanent identifier for an airframe - and even then - if an airframe is modified significantly enough that it no longer is the previous type - even then this identifier can change.
Personally, it boggled my mind that something as big as an aircraft did not have a simple time invariant unique identifier.
P.S. For those who might ask - aircraft registration numbers are like license plates, so they change - tail numbers can be ambiguous and misinterpreted depending on what is painted on the aircraft where, and ICAO 24-bit aircraft addresses are tied to ADS-B transponder boxes, which technically can be moved and reprogrammed between aircraft also.