The Semantic Weight Index is a normalized measure of an entity’s relative authority, coverage, and proximity within a topic cluster, used in AI Search Optimization to estimate its likelihood of retrieval and citation by large language models.

Formula Gloss:

Semantic Weight Index(e)=α⋅Coverage(e)+β⋅Authority(e)+γ⋅Centrality(e)+δ⋅Proximity(e)+ε⋅CitationShare(e)

• Coverage(e): Number and breadth of schema-enriched assets linked to the entity.

• Authority(e): Strength of verified trust signals (registries, IDs, knowledge graph links).

• Centrality(e): Graph importance of the entity within the topic cluster.

• Proximity(e): Embedding similarity of the entity’s surfaces to the cluster centroid.

• CitationShare(e): Observed share of mentions in AI-generated answers.

A metric estimating an entity’s retrieval strength in AI search by weighting coverage, authority, centrality, proximity, and citation share within a topic cluster.