Solitonic behaviour conjecture for discrete dynamical systems from general whurl relations

The loops around the cylinder are called whurls, and a whurl relation is the transformation $R$ on the parameters of adjacent whurls that preserves boundary measurements. In the mixed-wires setting, the corresponding carrier action is given by tropicalizing the whurl relations, with $(+,\times)\mapsto(\min,+)$. Solitonic behaviour conjecture. The discrete dynamical systems arising from general whurl relations exhibit solitonic behaviour. This conjecture proposes that the box-basket-ball systems associated with whurl relations having wires in both directions retain the soliton-like dynamics known from box-ball systems with uniformly oriented wires; the supplied text gives no evidence of resolution.