I'll talk about a new way to encode paracyclic structures (a combinatorial structure in Waldahausen's s-dot construction). This new way is through sheaves on broken cycles. This stack also parametrizes families of certain symplectic manifolds, so this new way allows us to see why the data for constructing Fukaya categories for exact 2-dimensional manifolds is equivalent to the data of a 2-Segal object (in the sense of Dyckerhoff-Kaparanov). A bonus is that we can prove theorems like: The K theory of the integers is equivalent to a Floer theory of Lagrangian cobordisms.