The phrase "are contingent on" is often used to describe the relationship between two things where one thing depends on the other. There are many synonyms for this phrase that can be used in different contexts. Some examples include "are subject to," "rely on," "hinge on," "rest on," "depend on," "be dictated by," "be determined by," "be influenced by," "be based on," and "be governed by." These phrases can be used interchangeably in most cases to convey the same basic meaning. However, depending on the context, one phrase may be more appropriate or effective than another.