We revisit the potential clustering property (cf. section 3.8.3) from the geometric measure theory perspective. Assume as always that the Lagrangian integral current $L$ is quantitatively almost calibrated, homologous to $L_{0}$, and equipped with Lagrangian potential $f_{L}$. Given constants $N\in\mathbb{N},A\in\mathbb{R}_{+}$, we say $L$ satisfies $(N,A)$-potential clustering, if

$$L=\sum_{1}^{N}L_{i},\quad f_{L}L=\sum_{1}^{N}f_{L_{i}}L_{i},$$

for quantitatively almost calibrated, closed Lagrangian integral currents $L_{i}$ with potential $f_{L_{i}}$, contained inside the support of $L$, such that the oscillation of the Lagrangian potentials have uniform bounds

$$\sup_{L_{i}}f_{L_{i}}-\inf_{L_{i}}f_{L_{i}}\leq A,$$

while for any $i>j$,

$$\sup_{L_{j}}f_{L_{j}}\leq\inf_{L_{i}}f_{L_{i}}.$$

Without loss of generality, we assume $\sup_{L_{0}}f_{L_{0}}-\inf_{L_{0}}f_{L_{0}}\leq A$ for the fixed Lagrangian $L_{0}$.

We will later be interested in uniform upper bounds on $N,A$. For now, we observe the robustness under limits: