Understanding Brand Authority Quotient (BAQ)

The governing measurement instrument for brand-level AI authority management, replacing binary CPQ for entities whose AI authority goal is attribute accuracy rather than pure citation probability. Formally: BAQ(B,Q_purchase,τ) = Σᵢ wᵢ × p(aᵢ_positive | q ∈ Q_purchase, τ) − Σⱼ vⱼ × p(aⱼ_negative | q ∈ Q_purchase, τ), where wᵢ are commercial weights of positive attributes and vⱼ are commercial weights of negative attributes, measured across the actual buyer query distribution Q_purchase. BAQ governs the Consumer Brand Authority Theorem (CBAT) – the formal extension of Byrum's Law to consumer and product brand management contexts.