Rodríguez's half-integer curvature conjecture for binary Bayesian networks

Let a bitnet be a binary Bayesian network equipped with its Fisher information metric, and let $\langle R\rangle$ denote its volume-averaged Ricci scalar. Rodríguez's conjecture. For any bitnet with Fisher information metric,

$$\langle R\rangle \in \tfrac{1}{2}\mathbb{Z}^+.$$

The paper resolves the conjecture only partially: it proves the claim for tree-structured and complete-graph bitnets, but disproves it in general by exhibiting loop counterexamples, including a double-collider network with $\langle R\rangle=36/5$.