Zhang, Yue: Structural Discoveries in the Collatz Conjecture: Modulo 64 Survivors, Confluence Points, and Energy Deviation

Abstract: This paper reports a series of new structures discovered in the iterative process of the Collatz conjecture (3x+1 problem). Based on the philosophical framework of "Energy Primordialism" previously proposed by the author, we identify, through manual computation and data analysis, eight special "survivor" residue classes modulo 64: 7, 15, 27, 31, 39, 47, 59, 63. These numbers exhibit exceptionally long trajectories, and their first-step energy release (i.e., the number of factors of 2 i