Detection Tools and Prime Functions: Security Assessment and Residual Limits

This note addresses potential risks of imitation claims regarding prime gap detection and generative functions. 
Using a local statistical framework, detection tools can reproduce up to ~98% of observed prime gap structures across ranges, 
but the remaining 1–2% residual variation is mathematically irreducible under current models. 

We demonstrate that while alignment within the statistical frame provides strong evidence of detectability and ordering, 
the residual component cannot be eliminated or exploited for practical cryptographic attacks. 
This establishes that prime detection and generative models, despite high coverage, 
do not compromise the safety of prime-based cryptography. 

The study concludes that residual order is intrinsic and robust against frame adjustments, 
and thus claims of complete reproduction or cryptographic vulnerability are unfounded.