Universal numerical threshold for optimal geometric gain

Establish a universal numerical threshold for the optimal geometric gain used by Geometric Gain Graph RAG across diverse underlying embedding models and retrieval settings.

Background

Geometric Gain Graph RAG models the relevance–novelty trade-off through the product of directional consistency and orthogonality, using the geometric gain function cosθ * sinθ. Although the continuous mathematical formulation has a theoretical maximum near a cosine similarity of 0.707, the authors distinguish this bound from an empirically universal optimum because real-world document embeddings occupy discrete and model-dependent spaces.

The unresolved problem is to determine a universal numerical threshold for optimal geometric gain that remains valid across different embedding models and corpora. Resolving it would provide principled threshold selection beyond the current empirically guided interval and could improve the portability of the retrieval framework.