Were both measurements done by the same method? Depending how they do it they can get different results, when surgery is recommended depends on a lot of factors, usually when it gets to >5.0, but it depends on your body size, family history, growth rate and other factors, that is why it is important to have a cardiologist that specializes in aortic issues, at 4.5 you should also consult with a thoracic surgeon, someone in a major medical center who has done the operation many, many times. Unfortunately for ascending aneurysms, it would be open heart but don’t get ahead of yourself, consult with the specialists, they will give you all the details and follow their advice.

All the best to you and feel free to continue asking questions, a lot of people in this forum have gone through what you are going through