Quantization of Ricci Curvature in Information Geometry

Carlos C. Rodriguez

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arXiv · 2603.10054

Quantization of Ricci Curvature in Information Geometry

Carlos C. Rodriguez

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Abstract

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. We extend the program to Gaussian DAG networks, where a sign dichotomy holds: discrete bitnets have positive curvature, while Gaussian networks form solvable Lie groups with negative curvature.

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Carlos C. Rodriguez. 2026-03-09. Quantization of Ricci Curvature in Information Geometry. https://arxiv.org/abs/2603.10054

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