Does Teachers Retirement have to recognize common law marriage in D.C. for spousal benefits?

If you were married under common law in any of the US States, the D.C. retirement office might be required to recognize it under the Full Faith and Credit clause of the Constitution, the same way that many Courts have now ruled that same sex unions performed in states which recognize them as valid must be afforded full faith and credit by other states, even if those states don't allow gay marriages.  However, I don't believe that there are any states which have common law marriages any more, although I suppose that if you established such a common law marriage many  years ago, when they were recognized in some states, you might still have a claim.  Also, the pension contract may define allowed beneficiaries or spouses to exclude common law spouses, which would not be a matter of Constitutional law, but rather the interpretation of a private contract.