Part I

The Physics of Search Have Shifted: From PageRank to Entity Authority

To an LLM, your brand is one entity. Your visibility depends on how strongly that entity is mathematically tethered to the specific problems your buyers are prompting about.

LLMs don’t read words — they map relationships. Models learn which brands co-occur with which problems, categories, and outcomes across the web.
High semantic density = high entity authority. The more frequently and consistently your brand co-occurs with your category, the stronger the association.
Classic ranking signals still matter, but the unit of competition is no longer just a page — it’s your entity.

Diagram contrasting Google's page-and-links algorithm with LLM retrieval built on entities and consensus — The physics of search have shifted: from page rank to entity synthesis. You're engineering a brand entity to be included in a mathematical synthesis.