Categorical Foundations and Higher-Order Topological Field Theory for Nucleonic Skyrmions

A categorical study for nucleonic topological phases is developed via extended topological quantum field theories and factorization algebras. Key results include the classification of nuclear spin systems up to unitary equivalence, the construction of higher-order invariants that fully capture the topological data, and the demonstration that anomaly inflow mechanisms guarantee the stability of topological phases under local perturbations.