The tightness conjecture for diffusion games

Let $G$ be a finite graph with an initial chip configuration. Call $(G,c_0)$ tight if the resulting diffusion-game process is eventually fixed or periodic with period length $2$.

Tightness conjecture. Every finite graph and initial configuration is tight.

The conjecture strengthens the question of whether every diffusion-game process is eventually periodic. It is known for paths, cycles, wheels, stars, complete graphs, and complete bipartite graphs, but remains open for general graphs.