A Resolution of the Collatz Conjecture via Archimedean Spiral Mapping and Topological Variance Decay
Year: 2026
Type: preprint
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}.
Author: HaoYue, Wang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169656137
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