Second video below the fold.
A direct republic is an organizational model utilizing select parts of a direct democracy and a constitutional republic. All members of a direct republic sign and agree the constitution/social contract. This contract states you will not engage in murder, rape, theft, and basic crimes against humanity. Once signed, the individual becomes their own representative and places social contributions directly into the funding pools for the social projects they approve of. All other laws are agreed to by adding modular pieces of law onto ones own palate of need.
This means the legislature is assembled in a DIY or build-a-bear fashion. Executives are, de facto, the individuals in charge of the projects you fund. The judiciary is self directed and handled by contract. Cases are settled in the arbitration services selected by contract, not by mandated courts with centralized statutes.