Effect of additional cycles in the food quiver on fixed points and convergence
Ascertain whether adding additional cycles that pass through a given vertex in the food quiver—such as introducing an M{content}M–Ice cream–Cookie three-cycle alongside the M{content}M–Cookie two-cycle—changes the fixed point or convergence rate of the coupled recursion defining the associated bi-∞ limits, and characterize any such changes.
References
On the theoretical side, Conjecture~\ref{conj:quiver-topology} asks whether the topology of the food quiver affects limit compositions. A natural first case is to compare the $\infty$-M{content}M Cookie computed from the two-cycle alone with the limit obtained when additional cycles pass through the Cookie vertex. Whether extra cycles alter the fixed point, accelerate convergence, or leave the limit unchanged is unknown.