The Flatness of Statistical Manifolds for Acyclic Graphs: Characterizing the Statistical Vacuum Einstein Condition | Synapse
March 3, 2026Open Access
The Flatness of Statistical Manifolds for Acyclic Graphs: Characterizing the Statistical Vacuum Einstein Condition
Key Points
The aim is to examine the curvature properties of statistical manifolds related to acyclic graphs and their compliance with the vacuum Einstein condition.
Derived exact curvature formulas for statistical manifolds.
Analyzed lattice fisher manifolds in relation to acyclic graphs.
Investigated the properties of trees as a specific case of acyclic graphs.
Proved that trees meet the vacuum Einstein condition G_ab = 0.
Provided exact curvature formulas that describe the nature of these statistical manifolds.
Abstract
Exact curvature formulas for lattice Fisher manifolds. Proves trees satisfy the vacuum Einstein condition Gₐb = 0.