VERY incorrect. The underlying relationship is a social COMPACT. In a CONTRACT one thing of value is exchanged for another. In a COMPACT, each parts with the same thing to get something of equivalent value. In the case of the United States, each individual parts with control or governance over part of his alienable rights in exchange for superior protection of his health, safety and security of his property.
The U.S. Constitution is a charter for an institution and a specific delegation of power which comes from the People who ratified the document through special conventions of individuals in each state elected specifically for that purpose. It is not a contract with the federal government which did not exist at the time and does not exist independent of the document. It is not a contract among the States as their legislatures did not ratify it. The People through special conventions did. In such a manner, the People were able to take power and authority that existed in the post-colonial State governments and re-vest it with a new national government.