What is “organic law”? Sounds like mumbo-jumbo to me. The Declaration absolutely did not begin the Republic. The Republic took form with the Constitution. Before that, it was states united under the Articles of Confederation. Before that, states united under the Continental Congress. Before that, colonies of the British empire.
There was no mystical bond running beneath the different arrangements rendering them one republic, eternal. Arguing otherwise cheapens the meaning of the Constitution, among other things. It also spits on the true place of the states, which us not as parts of an organic whole but entities unto themselves. They are the real thing, the underlying thing, not the Republic.
The Organic Laws of the United States of America can be found in Volume One of the United States Code which contains the General and Permanent Laws of the United States. U.S. Code (2007) defines the organic laws of the United States of America to include the Declaration of Independence of July 4, 1776, the Articles of Confederation of November 15, 1777, the Northwest Ordinance of July 13, 1787, and the Constitution of September 17, 1787.