Unveiling the Unseen Syntax: A Frequency-Based Seed Theory for the Traveling Salesperson Problem

This article documents the derivation of a novel heuristic framework for the Traveling Salesperson Problem (TSP). By shifting the focus from global permutation searches ($O(N!)$) to a localized "One-to-One" seed frequency analysis based on the initial distance vector, we demonstrate that the "unseen syntax" of a symmetric distance matrix can be decoded in polynomial time. Through a series of increasingly complex matrices—ranging from 6 to 100 cities—we prove that the global optimum is often hidden within a finite set of "starting combinations" determined by the unique mileage values of the primary node.