Abstract: Building on the result from the second talk, where we established the relation A = B, we will introduce a third class, defined as a sum over trees decorated with Omega classes (also known as Chiodo classes), and demonstrate that this new class is equal to the A-class and therefore the B-class. This class originates from a formula we conjectured representing quantum tau functions in the framework of quantum DR hierarchies. We will discuss this formula, and if time permits, present its recently discovered proof.