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 to 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. For detailed information on market arbitration, see The Machinery of Freedom, by Dr. David Friedman. 
Crimes are considered a breech of contract. This means that your rights are secured and enforced by contract. Some contracts may be very stern; others very lenient. Because one chooses their own penalties based on enforcement contract availability, exhaustive rights protection isn't required. In-group adjudication was agreed to prior to incident. Out-of-group adjudication is handled by your law service provider.