While memory effects emerge from systems of wildly varying lengthscales and timescales, the reduction of a complex system with many interacting elements into one simple enough to be understood without also losing the complex behavior continues to be a challenge. Here, we investigate how bistable cylindrical origamis provide such a reduction via tunably interactive memory behaviors. We base our investigation on folded sheets of Kresling patterns that function as two-state memory units. By linking several units, each with a selected activation energy, we construct a one-dimensional material that exhibits return-point memory. After a comprehensive experimental analysis of the relation between the geometry of the pattern and the mechanical response for a single bit, we study the memory of a bellows composed of four bits arranged in series. Since these bits are decoupled, the system reduces to the Preisach model, and we can drive the bellows to any of its 16 allowable states by following a prescribed sequence of compression and extension. We show how to reasonably discriminate between states by measuring the system's total height and stiffness near equilibrium. Furthermore, we establish the existence of geometrically disallowed defective stable configurations that expand the configuration space to 64 states with a more complex transition pattern. Using empirical considerations of the mechanics, we analyze the hierarchical structure of the corresponding diagram, which includes Garden of Eden states and subgraphs. We highlight two irreversible transformations, namely shifting and erasure of defects, leading to memory behaviors reminiscent of those observed with more complex glassy systems.