Collatz Conjecture: Unresolved Despite Cayley Graph and Digit Pattern Approaches — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Collatz remains unsolved; recent work explores automorphic Cayley graph structures and symbolic digit patterns, with no breakthrough proof. | MATH: Collatz map T(n) = n/2 if even, (3n+1) if odd; trivial cycle 4→2→1→4; arXiv:2008.13643v8 claims proof via Cayley colour graphs and decidability of an+b conjectures, but unverified. | CONNECTION: The trivial cycle 4→2→1 has ratio 1:2:4 (powers of 2, base-2 symmetry); branching at c=4 suggests a binary tree structure — but no explicit golden ratio, 0.618, 0.786, or base-60 link appears in the findings. The automorphic graph approach hints at lattice/root-system analogies (Cayley graphs of groups), but no crystallographic symmetry is explicitly stated. | DEPTH: 3 — The findings are meta-commentary (YouTube videos, a Lean kernel vulnerability hoax) plus one unverified preprint. No new verified equations, constants, or geometric harmonies emerge. The Collatz structure (2-adic dynamics) has deep ties to 2-adic integers and ergodic theory
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026collatz,
title = {{Collatz Conjecture: Unresolved Despite Cayley Graph and Digit Pattern Approaches — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23553688},
url = {https://zenodo.org/records/23553688},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collatz Conjecture: Unresolved Despite Cayley Graph and Digit Pattern Approaches — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23553688
UR - https://zenodo.org/records/23553688
AB - FINDING: Collatz remains unsolved; recent work explores automorphic Cayley graph structures and symbolic digit patterns, with no breakthrough proof. | MATH: Collatz map T(n) = n/2 if even, (3n+1) if odd; trivial cycle 4→2→1→4; arXiv:2008.13643v8 claims proof via Cayley colour graphs and decidability of an+b conjectures, but unverified. | CONNECTION: The trivial cycle 4→2→1 has ratio 1:2:4 (powers of 2, base-2 symmetry); branching at c=4 suggests a binary tree structure — but no explicit golden ratio, 0.618, 0.786, or base-60 link appears in the findings. The automorphic graph approach hints at lattice/root-system analogies (Cayley graphs of groups), but no crystallographic symmetry is explicitly stated. | DEPTH: 3 — The findings are meta-commentary (YouTube videos, a Lean kernel vulnerability hoax) plus one unverified preprint. No new verified equations, constants, or geometric harmonies emerge. The Collatz structure (2-adic dynamics) has deep ties to 2-adic integers and ergodic theory Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -