Block Format Solves the Collatz Conjecture

Blocks are unit convergence between two consecutive odd numbers formed according to the three x plus one conjecture rules. The left odd number is the left hook, L, and the right odd number is the right hook, R. They include even numbers between their boundaries. They are divided into families (F1 = 5, 11, 17, … & F2 = 1, 7, 11, … & F3 = 3, 9, 15, …) and groups based on their group length (The number of the middle-even numbers between the two hooks). Blocks are taken individually and placed beside each other, similar to the domino tiles play, which, by their formulation, satisfies the conjecture rules. Formed chains reach number one in the convergence mode or continue generating odd positive numbers infinitely according to the generation mode. The final convergence to number one is reached because these blocks have all the positive integers included as left hooks (L1, L2, L3), and all the F1 and F2 odd positive numbers are included as right hooks (R1 and R2). Block rules mandate that a single left hook produces only one right hook. Accordingly, no looping or entanglement (Joining and consequent splitting) between chain branches would occur. Statistics show that R cannot increase infinitely. Repeated oscillation up and down without reaching number one would also violate the statistics. Statistics reveal that blocks of various lengths have a strict occurrence and repetition sequence along the positive integer series. Block lengths can extend infinitely, and each block length repeats its occurrence infinitely. In the generation mode, blocks are attached in reverse order to the conjecture/convergence rules. According to the rules, all positive integers can be generated starting from number one. Multiple sequences and clusters of specific block lengths occur according to specific rules and cannot continue infinitely.