When two or more combat simulations are federated, differences in the ways they represent and reason about the world and how they communicate state changes can provide artificial advantages that lead to unfounded outcomes. Simulations are simplified representations of the real world that preserve detail and data where necessary to support their intended purpose and use abstractions where data is unavailable or in secondary areas. Such design decisions are valid when the simulations will be used as intended. However, when multiple systems, each of which have a unique purpose and supporting design, are combined in novel uses, their simplifying assumptions can overlap in ways that are not complementary and may result in invalid system interactions. Federated simulation events must minimize such occurrences to provide realistic results. However, this is much easier said than done; invalid interactions are typically caused by factors that can be deeply ingrained within each individual simulation system. Differences between these fundamental elements often only become obvious when the internals of the individual simulations are contrasted with each other. To achieve a fair fight, the simulations must be founded on compatible object models that preserve sufficient semantic equivalence between world models. The algorithms that form the basis for individual system reasoning must provide equivalent results across the interacting systems. The individual system environmental representations must be sufficiently correlated so that the potential for interaction between world objects is equivalent for all world objects. This paper considers these three fundamental characteristics of simulation systems: object models, reasoning algorithms, and environmental representations, from the perspective of the cross-system equivalence required to enable valid interactions. The general nature of the problem is defined, procedures to detect incompatibilities are developed, and strategies to prevent invalid interactions are proposed.