Question

what must the united states guarantee to every state in the union

Answer 1

look at the preamble! http://www.law.cornell.edu/constitution/preamble

Answer 2

The United States shall guarantee to every state in this union, a republican form of government, and shall protect each of them against invasion; and on application of the legislature, or of the executive (when the legislature cannot be convened), against domestic violence.
http://avalon.law.yale.edu/18th_century/art4.asp