The logical solution of the Syracuse conjecture

The conjecture of Syracuse (better known as the Collatz conjecture) is one of the many mathematical conjectures still waiting for proof. In this essay it is addressed from a completely different point of view than many previous attempts, by highlighting some of its features. From one of these features takes its cue a process that leads to a theorem whose proof solves the conjecture in a complete and definitive way. The theorem allow us to replace the cycles obtained applying the algorithm of Collatz with the cycles of links, transforming their oscillating sequences in monotone decreasing sequences, which, after a finite number of steps (very low), fall to 1 always respecting the final cycles {10; 5; 4; 2; 1} or {7; 5; 4; 2; 1}. With few steps we exit the maze, we reach sea level from high altitudes and we tame the crazy lift of a very high skyscraper. The solution of the conjecture of Syracuse reveals the magical harmony of odd numbers and opens new horizons to the number theory. The essay, accompanied by figures, contains the charts of links odd numbers from 5 to 2999 and the algorithm that allows you to calculate them. by aid of a desk calculating machine, following the algorithm, is possible to discover the magic of odd numbers hidden in this marvelous conjecture.