If Chopper has Hampered played on him, which states that a characters dice can not be modified, do the effects of Salvaged Arm or 3PO (or other effects that increase the value of a die) work?

The way I understand the rules the term modified would apply only to blue sides and would not indicate modification of a value in general, but I could see arguments the other way. For example, Vigilance prevents focus even though it does not explicitly use the word focus, relying instead on the fact that it’s obvious that focus is turning a die. In a similar manner, it is obvious that increasing the value of a die is modifying it.

Changing the value of a die is not modifying a die. Focus likewise is a specific type of die side which allows a player to turn a die and Vigilance is worded the way it is so that it prevents all turning of dice not just focuses.