This research establishes a mathematical property proving that all AI-generated texts inevitably converge to a specific statistical pattern, creating a detectable fingerprint.

• All AI-generated texts must eventually reflect the model's average entropy
• Long synthetic texts fall into a mathematically defined "typical set"
• This property persists across different models and generation methods
• Provides theoretical foundation for more reliable AI text detection systems

For security professionals, this research offers a robust mathematical framework for identifying AI-generated content, potentially addressing deepfake text concerns and improving authenticity verification in digital communications.

Slaves to the Law of Large Numbers: An Asymptotic Equipartition Property for Perplexity in Generative Language Models