Library on heuristic and structural approaches to prime divisibility in integers, Vol.2

This preprint serves as the second volume in an ongoing independent research project mapping localized structural shortcuts and digit-displacement heuristics along the integer number line. Following the foundational single-digit mechanics established in Volume 1, Volume 2 formalizes a predictable direct-quotient extraction engine designed specifically for five-digit architectures divisible by 11. By evaluating the structural wave balance of an input via alternating sums, the system bifurcates integers into a Cancellation Zone (H_r = 0) and a Non-Cancellation Zone (H_r > 0). It demonstrates how direct spatial contraction combined with a dynamically scaled subtraction gate successfully yields exact multipliers, completely bypassing standard iterative division methodologies.