Ω Relational Geometry — Addendum A: Local Structural Perturbations of Nested Relations

This note presents a small structural observation extending the Ω Relational Geometry framework. The experiment examines how the invariant μ (average containment depth) behaves under local Tamari rotations of Ω-trees representing nested relational containment. All ordered Ω-trees for n = 6–8 leaves were enumerated and each single Tamari right-rotation was applied. The resulting change Δμ = μ(T′) − μ(T) was recorded. Figures included in this note visualise: • the distribution of Δμ under local structural perturbations • the fraction of rotations that preserve μ • the scalar field of μ across the associahedron adjacency graph The purpose of this note is purely structural. No interpretive claims are made. It accompanies the original Ω Relational Geometry paper which defines the nested relational framework and invariant μ.