The great fundamentals most likely refers to the general fundamentals of the Plymouth Colony. The General Fundamentals of the Plymouth Colony were a prelude to the American Constitution and Bill of Rights. They requested a representative form of government as well as personal rights for citizens.
The General Fundamentals included language that was very similar to language found in the Declaration of Independence. Both the Declaration of Independence and the General Fundamentals made reference to citizens having a say in what laws get enacted against them; having a say requires having representation in government. This concept of representation also found its way into the Constitution of the United States, which set up a bicameral representative government, with a House of Congress and a Senate.
The general principles also make reference to equal access to justice for all, which is similar to the Declaration of Independence's reference to "all men [being] created equal." The concept of equal access to justice also appears in the Fifth Amendment to the Constitution. The Fifth Amendment includes the Due Process Clause, which ensures that the same process applies to criminal proceedings against everyone. The Fifth Amendment also guarantees the right not to testify against one's self, which means that the prosecution cannot subpoena a criminal defendant.