Let's take California for example. You have the State of California (
http://www.ca.gov/).
But then take a look at their legislatures. They are not the "State of California Legislature" but rather the "California State Legislature".
http://www.legislature.ca.gov/
A state shall not make anything but gold or silver coin a tender in payment for debts. Article 1 Section 10. Yet the provision only applies to states, not corporations. Whenever payment for debts is performed by California I believe that it is through the issuance of drafts (checks) by the State of California which drafts cannot be converted to gold or silver coin. If the State of California is a corporation then there is no violation of the constitutional mandate.
Want to see some serious dancing? Try demanding an answer from the state or a judge whether the State of [your state] is a corporation. They will not answer.
So what I am looking for are facts that substantiate, disprove, or give evidence one way or another on whether or not the State of [whichever] is a corporation.