Abstract This paper presents a complete mathematical resolution to the Collatz (3n+1) Conjecture. By diverging from traditional discrete number theory, we construct an Archimedean spiral parametric mapping that defines a non-linear state transformation within a high-dimensional symmetric topology. We prove that all arbitrary initial integer states induce a Markov chain iteration whose global topological variance strictly dissipates. Under these deterministic limits, the trajectory is mathematically bounded from infinity and globally converges to the unique stable attractor 4, 2, 1.
Wang Haoyue (Sat,) studied this question.