What the primer covers
This primer explains the formulas in the Generative Brand Mention Framework (GBMF) with worked examples. Each formula section covers the definition, the intuition, a step-by-step breakdown, a concrete worked example, and a small Python implementation. No prior familiarity with mathematical or academic notation is assumed.
The worked example throughout is the synthetic brand Acme Analytics, which produces the headline scores MV 52 / MA 67 / MS net +25 from a 30-prompt, 5-engine measurement. The full per-prompt per-engine mention rates are published as supplementary data alongside the canonical paper, so every figure here can be re-derived from an open dataset.
This page summarises the primer — the full document is the PDF
Formula derivations, edge-case handling, extended Python implementations, and full notation reference are in the PDF only.
Download the full primer (PDF) →Framework overview
Before working through each formula, here is the entire framework in plain English.
MV (brand-mention visibility) answers: how often does this brand appear in AI answers to relevant questions?
A brand with a high MV appears consistently across many different prompts and many different AI engines. A brand with a low MV is rarely mentioned. MV is a detection measure over the full declared prompt set. It does not condition on anything.
MA (brand-mention alignment) answers: when AI does mention this brand, how accurate is what it says?
A high MA means AI describes the brand correctly: right category, right pricing, accurate differentiators, and correct use cases. A low MA means AI gets the facts wrong. MA is a conditional measure; it conditions on the brand being mentioned.
MS (brand-mention sentiment) answers: when AI does mention this brand, does it speak positively or negatively about it?
A positive MS means AI characterisations favour the brand. A negative MS means AI characterisations criticise it. The unit of analysis is the brand-directed characterisation, not the overall tone of the response. MS is the second conditional measure: it also conditions on the brand being mentioned. It does not condition on whether the description was accurate.
Why three measures and not one. A brand can be mentioned yet described inaccurately. A brand can be described accurately yet positioned unfavourably. A brand can be visible, accurate, and well-characterised, while another brand in the same category sits at every other combination of those three properties. The three measures separate properties that prior instruments collapse or omit.
What the framework does not do. The formulas alone do not explain why a brand has a given score or prescribe how to improve it. Those questions are handled through diagnostic reports and practitioner interpretation built on the measures. The framework also does not establish that AI representation predicts commercial outcomes. It provides a reproducible measurement that brands, researchers, and agencies can use to track change over time and compare positions across competitors.
How to cite
Aiviara Research. (2026). The Generative Brand Mention Framework: A Formula-by-Formula Primer. https://aiviara.com/research/gbmf-formula-primer/