What project management term would you associated with a predetermined budgetyou're your program?

Program governance refers to the framework of policies, decision rights, and accountability structures used to manage the program, not a budget limit.

In project and program management, a constraint is any factor that limits the options available to the management team, including predefined limits on budget, schedule, or scope. A budget set externally before the program plan is developed restricts what the program can accomplish and how resources can be allocated. Constraints must be acknowledged and managed throughout the program lifecycle.

A cost baseline is the approved version of the time-phased project budget, which is developed during planning - it is not the same as an externally imposed predetermined budget.

An assumption is something believed to be true for planning purposes without proof; a fixed budget is a known and imposed restriction, which is a constraint, not an assumption.