Elementary Moves on Ideal Webs, Local Monodromies on Hitchin Fibrations, and Tropical Mutations on $\mathrm{K_0}$ Groups

This paper builds on the work of Goncharov by studying the correspondence between topological spectral covers constructed from generic $A_{m-1}$-webs with rank $m\ge2$, Hitchin spectral curves over good Hitchin loci, and the Grothendieck groups $K_0(\mathcal{D}_Γ)$ associated with the quivers with p