Quantization of Ricci Curvature in Information Geometry

ArXi:2603.10054v1 Announce Type: cross In 2004, while studying the information geometry of binary Bayesian networks (bitnets), the author conjectured that the volume-averaged Ricci scalar computed with respect to the Fisher information metric is universally quantized to positive half-integers: in (1/2)Z. This paper resolves the conjecture after 20 years. We prove it for tree-structured and complete-graph bitnets via a universal Beta function cancellation mechanism, and disprove it in general by exhibiting explicit loop counterexamples.