Think about it....The engine is a late 1999 model.. The mower should be a 2000 or 2001 model. And it is a garden tractor[GT] and not a lawn tractor [LT] so the model number will start with 14 and will have a H in it for the 46 deck.
Probably likely a 14AJ848H131 or less likely a 14AJ849H131