Byrum’s Dominance Inequality

Coined Term • 2026

Byrum's Dominance Inequality

The formal condition an entity must satisfy for sustained AI citation dominance

Status

Coined by Joseph Byrum

Year Introduced

2026

Domain

Entity Engineering

Term Type

Operational Framework

Understanding Byrum's Dominance Inequality

The formal condition for sustained AI citation dominance: Sε,flow + Sε,stock > Eε(γ) + Sα. The sum of an entity's signal construction rate (Sε,flow) and accumulated structural advantage (Sε,stock) must exceed the sum of the effective decay rate of the AI's parametric memory (Eε(γ)) and the aggregate competitive signal construction rate (Sα). When satisfied, CPQ rises toward and maintains the Ontological Dominance threshold.

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Frequently Asked Questions

What does Byrum's Dominance Inequality state?

The inequality states that sustained AI citation dominance requires the sum of an entity's signal construction rate and accumulated structural advantage to exceed the sum of the AI's parametric decay rate and the aggregate competitive signal construction rate.

What happens when the inequality is not satisfied?

When the inequality is violated, CPQ declines toward the system's prior probability across training cycles — eventually falling below the CPQ citation threshold and losing unhedged citation status.

What are the four components?

S_flow (signal construction rate), S_stock (accumulated structural advantage), E_θ (effective parametric decay rate), and S_c (aggregate competitive signal rate) — the four inputs that determine whether CPQ rises, holds, or decays.

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