Sidorenko property of vector configurations of bipartite graphs

Prove or disprove that for every k-vertex bipartite graph H and every prime power q, the linear configuration Vec_q[H]⊆F_q^k is Sidorenko.

Background

The paper explains that the Sidorenko property for a bipartite graph implies the Sidorenko property for its associated vector configuration Vec_q[H]. It then proposes the converse-direction-style assertion that all vector configurations arising from bipartite graphs have this property, even when the graph itself is not assumed to be Sidorenko.

References

For every $k$-vertex bipartite graph $H$ and prime power $q$, the linear configuration $Vec_q[H] \subseteq \mathbb F_qk$ is Sidorenko.

— Generic solutions to symmetric linear equations  (2610.02177 - Frederickson et al., 1 Oct 2026) in Conjecture, Section 1, subsection “Linear configurations and graphs”