Basis conjecture for curvature-zero functions on positroid subdivisions

Let $\Delta_{k,n}$ be the hypersimplex, and let $e_J\in\Delta_{k,n}$ range over its $\binom{n}{k}-n$ nonfrozen vertices. For each such vertex, let $\rho_J$ be the corresponding function. Consider the space of piecewise-continuous functions on $\Delta_{k,n}$ that have zero curvature over the maximal cells of some positroid subdivision of $\Delta_{k,n}$. Basis conjecture. The set of functions $\rho_J$, where $e_J\in\Delta_{k,n}$ ranges over all $\binom{n}{k}-n$ nonfrozen vertices, defines a basis for this space. The conjecture would connect the boundary-operator description of curvature-zero functions with positroid subdivisions and generalized Feynman diagrams; the source leaves its investigation for future work, in the context of Lafforgue's work and related developments.