Structural Determinism in Computational Hardness: A Counter-Argument to the Randomness Assumption in SETH via Fermat-Brahmagupta (FB) Locking

This work presents a structural counter-example to the 'unstructured hardness' assumptions underlying the Strong Exponential Time Hypothesis (SETH). By demonstrating a deterministic 'Determinant Lock' and a division-free transition mechanism in Fermat factorization, we show that the solution space is highly anisotropic. This finding challenges the universality of SETH, proving that structural shortcuts exist where randomness was previously assumed.