In this paper Syracuse Conjecture (better known as Collatz Conjecture or 3n+1 problem) is approached by highlighting some of its features. One of them suggests a process that leads to Theorem 2n+1 whose proof solves the conjecture in a complete e definitive way. Theorem 2n+1 allow us to replace the Collatz cycles with the cycles of links, transforming their oscillating sequences in monotone decreasing sequences. 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. By Theorem of Independence we can go on to reach very high horizons, and when we decide go back to 1. I prove also that Syracuse Conjecture is not fully verifiable, because there are an infinitum of possible cycles, but it is fully demonstrated, and we claim surely that its initial assertion is true. In other words: BIG CRUNCH is always possible, but BIG BANG has no End. [Publisher's text].
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