The American colonials actually declared their independence from Britain on July 2, 1776. Americans today celebrate independence day on July 4th - the day the Founding Fathers got around to filling out the paperwork on their revolution.
Only a couple of the Founding Fathers signed the Declaration of Independence on July 4th - most didn't sign until August, and one particularly cautious revolutionary didn't add his signature until the war was almost over.
Counterfeiting and treason are the only crimes mentioned in the Constitution.