Complete blueprint of collatz

Complete working blue print of collatz. Complete logical frame work and proof to be translated in mathmetical proof. Forgive my handwriting and typos. I haven't tested it rigorously yet but you can. If found any mistake map positions yourself and correct it, though i hope you won't found any. Side note: you don't need to calculate the number itself, positions work quite fine. Number calculation is only for if you want to check where you are standing. Every position of 5mod8 map back to original function. Path calculation is possible. New picture is attached with previous post stating hidden structure of collatz