The Index Spread Law in Prime Multi-Link Additive Frameworks

Abstract

This paper presents a fundamental expansion of the Sherehii Moving Frame Method, introducing the Prime Index Spread Law. By mapping localized multi-link additive frames directly onto the sequential indices of the prime sequence (p_n), we isolate an invariant geometric constraint: the index distance (spread) between the boundaries of an adaptive frame consistently resolves into a prime number. Empirical and computational verifications are executed for consecutive and non-consecutive macro-nodes, including p_36=151, p_50=229, p_100=541, p_200=1223, and p_10000=104729. The results demonstrate that multi-link frames dynamically scale and expand their components to maintain systemic stability bounded by P/k > sqrt(P), operating as a self-correcting arithmetic matrix.