Citation Persistence Model
The Citation Persistence Model defines how authority compounds and decays within the 411bz framework. It separates authority into two orthogonal layers — Structural Authority as a fast-moving leading indicator and Economic Authority as a slow-moving lagging indicator — and models citation recurrence, nonlinear decay, momentum dynamics, and permanent peak tracking.
The Dual-Layer Authority Model
Authority is not a single number. It operates across two layers that move at different speeds and serve different predictive functions. Neither layer alone captures the full picture. Together they define an entity's citation trajectory.
Structural Authority gets an entity cited. Economic Authority keeps it cited.
Citation Persistence Index
The Citation Persistence Index (CPI) measures the recurrence and durability of AI citations over time. A single citation event does not build economic authority. Only recurring citations — sustained across multiple observation windows — compound into durable authority capital.
Recurrence Measurement
CPI tracks whether an entity is cited repeatedly across distinct query sessions, time windows, and AI systems. Isolated citations have minimal persistence value. Repeated citations across independent contexts compound into structural permanence.
Observation Windows
Citation events are aggregated across rolling observation windows. Short-term recurrence (7-day) validates immediate relevance. Medium-term recurrence (30-day) establishes category presence. Long-term recurrence (90-day) signals durable authority.
Nonlinear Decay Model
Authority does not decay linearly. The Citation Persistence Model defines three distinct decay phases, each with different erosion characteristics.
Phase 1: Grace Period (0–30 days)
Full authority is preserved with minimal erosion. Recent citations carry maximum weight. The grace period exists because citation impact propagates through AI knowledge systems with inherent latency. Authority earned within the last 30 days is treated as fully active.
Phase 2: Early Erosion (30–60 days)
Gradual decline begins as citation recurrence weakens. If new citations do not reinforce the existing authority, EAS begins to erode. The rate of erosion accelerates as the observation window extends without reinforcement. Entities with high CPI resist early erosion more effectively.
Phase 3: Accelerated Decay (60+ days)
Steep authority loss occurs when citations are not reinforced beyond the 60-day threshold. The decay curve steepens nonlinearly. Authority that was built over months can erode substantially within weeks if citation recurrence ceases entirely. Only sustained structural authority (high SAS) slows this phase.
Decay is not punishment. It is the natural consequence of citation systems favoring recency and reinforcement. Authority must be maintained, not merely established.
Peak Tracking
The Citation Persistence Model maintains permanent lifetime records for both structural and economic authority peaks.
- Structural Peak (SAS Peak): The highest SAS score ever recorded for the entity. This represents the maximum structural readiness achieved. It is a permanent record that persists regardless of subsequent score changes.
- Economic Peak (EAS Peak): The highest EAS score ever recorded. This represents the maximum durable authority achieved. Economic peaks are harder to reach and indicate sustained citation dominance over extended periods.
- Peak Divergence: The gap between current scores and historical peaks provides diagnostic information. A large divergence between current SAS and SAS Peak indicates structural regression. A large divergence between current EAS and EAS Peak indicates authority erosion.
Peaks are never reset. They serve as permanent benchmarks against which current authority is measured.
Frequently Asked Questions
What is the difference between Structural Authority and Economic Authority?
Structural Authority Score (SAS) is a fast-moving leading indicator that measures current AI citation readiness across 8 dimensions. Economic Authority Score (EAS) is a slow-moving lagging indicator that measures citation persistence, brand gravity, and accumulated authority capital. SAS reflects what you can be cited for today. EAS reflects how durably established that authority is over time.
How does authority decay work in the Citation Persistence Model?
Authority decays nonlinearly across three phases. The grace period (0–30 days) preserves full authority with minimal erosion. Early erosion (30–60 days) introduces gradual decline as citation recurrence weakens. Accelerated decay (60+ days) produces steep authority loss when citations are not reinforced. Only sustained, recurring citations prevent long-term decay.
What is Momentum Authority and does it persist?
Momentum Authority is a temporary acceleration triggered by viral citation spikes or sudden surges in AI references. It can push authority above historical peaks temporarily, but decays rapidly on its own. Momentum does not convert to durable authority unless the underlying citations are sustained and recurring. Only persistent citation converts momentum into lasting Economic Authority.
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