A Rigorous Framework for the Collatz Conjecture
Abstract
We analyze Collatz by restricting to $A = \{N \text{ odd}: v_2(3N+1) \le 6\}$, containing $63/64$ of odd integers. We prove equivalence to full conjecture, characterize $A$ via congruences, establish growth constraints, develop Markov models, and synthesize with Tao's result and 2-adic theory.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical Dynamics and Fractals
Advanced Mathematical Theories
Publication details
- Publication date
- 10 February 2026
- Language
- EN
- Document type
- Preprint