WordNet sense 1 ((law) an agreement or concession made by parties in a judicial proceeding (or by their attorneys) relating to the business before the court; must be in writing unless they are part of the court record):

judicial admission

WordNet sense 2 (an assumption on which rests the validity or effect of something else):

condition, precondition

WordNet sense 3 (a restriction that is insisted upon as a condition for an agreement):

specification