Radical Transitions in Generic Design: Frame Semantic Hypergraphs and Topological Diagrams in C/K Theory

Abstract Generative AI appears to be forcing a radical transition whose outcome cannot yet be known, and past transitions in the technics of language suggest that utopian and dystopian outcomes tend to arrive together. Drawing on the linguistic turns that followed those transitions, we approach design as the composition of conceptual materials grounded in language use, guided, in Sellars’s reading of Plato, by the soul as craftsman. We supplement C/K (Concept-Knowledge) design theory with frame semantic hypergraphs built in TypeDB (FSN-TDB), in which C becomes a schema of framed possibilities and K their instantiation by textual evidence, and we extend this to graph-directed design execution. We then argue that C/K Topos theory, built around creative preservation, cannot address radical transitions in which concepts and even data change, and show how thought experiments and impossible figures analyzed through sheaf cohomology can extend it. Frame semantic hypergraphs and topological diagrams prove complementary: the first show discrete structure, the second continuous coverage, strain and gaps. We conclude that design can right an imbalance between the correctness of the picture and the correctness of the performance. The paper was itself synergistically designed with an AI participant.