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.

Background

The authors introduce homological foods governed by cycles in a directed food quiver and conjecture that quiver topology influences limits.

For the M{content}M–Cookie system, they suggest comparing the limit from the two-cycle alone with the limit when additional cycles pass through the Cookie vertex, but they note that the outcome is currently unknown.

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.

The $\infty$-Oreo$^{^\circledR}$  (2604.00435 - Bosca, 1 Apr 2026) in Section 6, Discussion