The Synchronization Bridge: A Proof of P=NP

This research presents a formal, constructive proof establishing that P = NP by resolving the "Complexity Gap" as a perspectival illusion. The proof centers on a deterministic, polynomial-time solution to the integer factorization problem, positing that its perceived difficulty arises from a dimensional misalignment between the search origin and solution coordinates. The author introduces a Modular Synchronization Sieve to discover a Telescopic Mapping k, which aligns the geometric properties of a target composite N to its arithmetic search space. By applying a novel Jump Identity, the algorithm enables factor discovery in O(1) iterations, effectively reducing the parabolic search field into a linear, polynomial calculation.