Bounded ${\mathfrak{s}\mathfrak{p}}_4$-laminations and their intersection coordinates

We introduce rational bounded ${\mathfrak{s}\mathfrak{p}}_4$-laminations on a marked surface $\mathbf{\Sigma }$ as a proposed topological model for the rational tropical points ${\mathcal{A}}_{S{p}_4,\mathbf{\Sigma }}({\mathbb{Q}}^{\mathsf{T}})$ of the Fock–Goncharov moduli space [FG06]. Our space consists of certain equivalence classes of ${\mathfrak{s}\mathfrak{p}}_4$-webs introduced by Kuperberg [Kup96], together with rational measures. We define tropical coordinate systems using the ${\mathfrak{s}\mathfrak{p}}_4$-case of the intersection number of Shen–Sun–Weng [SSW25], and establish a bijection using the framework of the graded ${\mathfrak{s}\mathfrak{p}}_4$-skein algebra. This provides a topological perspective for Fock–Goncharov duality for ${\mathfrak{s}\mathfrak{p}}_4$.