Cosmological correlators for power-law FRW spacetimes take the form of twisted integrals associated to hyperplane arrangements and evaluate to interesting generalized hypergeometric functions. Using the framework of relative twisted cohomology, we identify a distinguished basis of cohomology and homology from the geometry of generalized unitarity cuts. Each generalized unitarity cut and basis element of (co)homology is associated to a combinatorial gadget called an acyclic minor (a type of decorated graph). In fact, the associated canonical differential equations can be computed purely combinatorially from these acyclic minors. Similarly, the acyclic minors control the combinatorics of sequential residue contours associated to the generalized unitarity cuts. Combining the combinatorics of the differentials and discontinuities (residue contours), we derive a graphical formula for the coaction on these hypergeometric functions in terms of the acyclic minors.