1. Introduction
When users ask an AI system for a list of recommended entities, the requested list size varies: "What is the best agency?" (N=1), "What are the top 3 agencies?" (N=3), "List 10 agencies" (N=10). Whether the AI system maintains a stable internal ranking that simply truncates at the requested size, or whether it generates fundamentally different rankings for different magnitudes, has practical implications for competitive positioning and AI visibility strategy.
2. Experimental Design
We submitted identical recommendation queries with systematically varied list-size parameters. The base query was held constant while the requested number of entities was varied from N=1 through N=10. For each response, we recorded which entities appeared, their ordinal position, and whether entities that appeared in shorter lists maintained their position in longer lists. The experiment was conducted in a single service vertical to control for domain-specific factors.
3. Results
3.1 Core Entity Stability
A set of core entities appeared consistently across all list sizes. The entity recommended at N=1 appeared at position 1 or 2 in every list size from N=2 through N=10. Entities appearing in the N=3 list were present in all subsequent list sizes, maintaining their relative ordering. This pattern indicates a stable internal hierarchy that is revealed progressively as the list size increases rather than regenerated for each magnitude.
| Query Magnitude | Core Entities Present | Position Consistency | New Entities Added |
|---|---|---|---|
| N=1 | 1 | Baseline | 1 |
| N=3 | 3 | High (position ±1) | 2 |
| N=5 | 4-5 | High | 1-2 |
| N=7 | 5-6 | Moderate | 1-2 |
| N=10 | 6-8 | Moderate | 2-4 |
3.2 The N=4 Gap
An anomalous finding emerged at N=4: no tracked entities from the core set appeared in one iteration of the N=4 query. This gap suggests that certain magnitude values may trigger non-deterministic behaviour or access different entity pools. The N=4 gap was not replicated in subsequent tests, suggesting it may represent stochastic variation rather than a systematic routing difference. However, it indicates that position stability, while strong, is not absolute.
3.3 Magnitude-Specific Source Shifts
At N=10, the source composition shifted. While N=1 through N=7 queries drew primarily from the model's parametric knowledge (training data), N=10 queries triggered a shift toward self-published listicle content and directory sources. This source-type shift did not displace core entities from their positions but did introduce new entities from different source categories into the lower positions of the expanded list.
4. Implications
The stability of core entity rankings across magnitudes suggests that achieving citation status at small list sizes (N=1 through N=3) confers positional advantages that persist as the query magnitude increases. Competitive displacement would require not merely adding content but actively displacing an anchored entity from the model's internal hierarchy — a significantly higher barrier than simply appearing in search results.
The N=10 source shift has strategic implications: entities that dominate directory and listicle sources may gain preferential access to expanded-list positions, even if they are absent from the model's core parametric rankings. This creates a dual-track positioning strategy where training-data presence secures core positions and directory presence secures expanded-list positions.
5. Limitations
The experiment was conducted on a single AI model at a single time point in a single service vertical. The N=4 gap anomaly remains unexplained and was not replicated. Entity rankings in AI systems may change with model updates, training data refreshes, and retrieval index modifications. The stability observed here represents a snapshot that may not persist across model versions.
6. Conclusions
AI models maintain stable internal entity rankings across query magnitudes from N=1 through N=10, with core entities occupying anchored positions that resist displacement from magnitude variation. The stability is strongest for top-ranked entities and decreases for lower positions. A source-type shift at N=10 introduces additional entities from directory sources without displacing core entities. These findings suggest that AI recommendation position, once achieved, carries a degree of structural persistence that favours incumbents.