From the succession of Collatz Personalized, the veracity of the same can be deduced

One of the problems of elementary mathematics, still unsolved, is the Collatz conjecture (after the mathematician Lothar Collatz). It concerns the following function between natural numbers: f: N→ N with f(N)= N/2 if N is even or f(N)=(3*N+1) if N is odd.By iterating the function several times, after a certain number of iterations we get the number 1 and continuing the iterations we have the cycle 1 → 4 → 2 → 1. Then the initial number N, in subsequent iterations, is multiplied by 3 (adding 1) and divided by 2, so that we have a succession of odd steps (when multiplying by 3 and adding 1) and even passes (when dividing by 2) that, after a certain total number of even passes bi and a certain total number of odd steps to, converges to 1.In my 2 previous papers, a custom sequence of the Collatz function has been defined, formulated on a modular basis and oriented to reduce the number of iterations required for convergence. Thanks to algorithmic coding and a diagrammatic structure, the method allows for simplified tracking of odd and even steps, with obvious computational advantages.In this work I also verify Theorem No. 6.2 of reference [1] and prove the same using the Theorem of the intersection of two lines in paragraph 5.