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This lecture covers the concept of dilute instanton gas approximation, focusing on the pre-factor, action, and gas approximation. The instructor discusses the perturbative corrections and the twisted partition function, emphasizing the avoidance of multi-instantons. The lecture delves into the validity of the dilute instanton and the twisted partition function, providing insights into the perturbative corrections and the twisted partition function. Various comments and explanations are given regarding the perturbative corrections and the twisted partition function, highlighting the importance of choosing the right parameters to avoid multi-instantons.