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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

Quantization of Ricci Curvature in Information Geometry

arXiv
Authors: Carlos C. Rodriguez

Year

2026

Paper ID

28585

Status

Preprint

Abstract Read

~2 min

Abstract Words

97

Citations

N/A

Abstract

In 2004, while studying the information geometry of binary Bayesian networks (bitnets), the author conjectured that the volume-averaged Ricci scalar <R> computed with respect to the Fisher information metric is universally quantized to positive half-integers: <R> 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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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.10054 [2] arXiv https://arxiv.org/abs/2603.10054 [3] Publisher https://arxiv.org/abs/2603.10054

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