Unverified Proof of Collatz Conjecture via Automorphic Cayley Colour Graphs — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Collatz conjecture remains unproven; a claimed proof using automorphic Cayley colour graphs exists but is unverified. | MATH: Collatz function: f(n) = n/2 if n even, 3n+1 if n odd. Conjecture: ∀n∈ℕ, iterates reach cycle 4→2→1. The arXiv paper (2008.13643v8) claims decidability of an+b conjectures and proof of 3n+1 via automorphic Cayley colour graphs, representing Collatz steps as walks over root paths to branching number c=4 in trivial cyclic root. | CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) found in these results. The automorphic graph approach may imply lattice or symmetry structures, but evidence is insufficient to confirm. | DEPTH: 2 — No verified breakthrough; the claimed proof is not peer-reviewed or widely accepted. The problem remains unsolved. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203689492
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