K-theoretic Persistent Cohomology

We develop K-theoretic persistent cohomology (KPCH): a principled extension of 1-parameter persistent (co)homology that equips the Grothendieck group of persistence modules with lambda-operations arising from exterior powers. This yields new, computable persistence layers that quantify concurrency among cohomology classes via interval intersections. We establish the core algebraic and stability results, provide an interval-calculus for efficient computation on barcodes, and demonstrate empirical benefits on graph filtrations, where KPCH separates patterns that standard additive H^p summaries such as total persistence cannot distinguish.