Data Structures and Algorithms

The Collatz Conjecture as an Information Compression Algorithm to the Ideal Bit

Authors: Yuriy Sunurov
Comments: 6 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present a proof of the Collatz conjecture through the framework of T0 Theory (Theory of Volumetric Time). Any positive integer n, represented as a binary information packet, undergoes deterministic compression toward the ideal bit gamma = 1. Operation n/2 lowers the T0-level by 1. Operation 3n+1 applied to odd n always produces an even number (proven by binary arithmetic), thus always returning to the compression path. The number 1 is the primordial source (entropy=0) to which all integers return. The main formula 1^(inf-1)/2^n = 1 encodes this as an axiom.
Category: Data Structures and Algorithms