Explore a comprehensive lecture on the invariants of manifolds from six dimensions, focusing on part four of the series. Delve into advanced mathematical concepts presented by Pavel PUTROV from ICTP during the School and Workshop on Gauge Theories and Differential Invariants. Learn about schematic faults, noncompact surfaces, two-corner configurations, and ship-like structures. Examine the intricacies of generating functions and their relationship to vector superior algebra. This in-depth talk, lasting over an hour, offers valuable insights for mathematicians and physicists studying high-dimensional manifolds and their invariant properties.