Interaction as Joint Constraint Satisfaction of Topological Operators in Basic Ontodynamics

We extend the operator formulation of Basic Ontodynamics by interpreting interaction as the joint satisfaction of closure constraints imposed by multiple topological operators on a common actualization flow. While an isolated node is described by a single operator O transforming an incoming flow J into an outgoing regime, systems of multiple nodes require a nonlinear joint operation O1 ⋆ O2. We show that the joint action J12 = (O1 ⋆ O2)(J) is generally non-additive and can be understood variationally as the flow configuration that minimizes the total deformation of the background subject to the simultaneous closure constraints of both operators. The resulting interaction energy functional measures the excess or deficit of deformation caused by the joint presence of the operators. Negative interaction energy corresponds to compatible compositions that lower the overall flow conflict (binding), while positive energy corresponds to incompatible compositions that increase conflict (repulsion). This framework treats forces not as externally imposed fields but as effective manifestations of the non-additivity and non-commutativity arising from joint constraint satisfaction. It provides a structural language in which matter can be understood as stable networks of operator compositions, while leaving the identification of specific compositions with known fundamental interactions as an open program for future work.