Collatz Conjecture Remains Unsolved Despite Topological, Formal, and Symbolic Advances — E8 Intelligence Research

This is the authors' abstract. We don't add key points for this paper.

FINDING: Collatz remains unsolved; recent work explores topological/ergodic frameworks, Lean formalization vulnerabilities, and digit-symbolic approaches, but no breakthrough. | MATH: Collatz map T(n)=n/2 if even, (3n+1)/2 if odd; no new constants/equations derived in these sources; arXiv 2601.03297 introduces a topology/σ-algebra where recurrence implies periodic orbit structure (no explicit constants given). | CONNECTION: None of the sources cite 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetries. The ergodic approach hints at measure-preserving dynamics but no explicit ratio or lattice link. | DEPTH: 2 — These are progress reports and a formalization bug, not substantive mathematical advances. The arXiv paper's topological framing is novel but lacks extracted constants or geometric harmony. No evidence of universal structure revealed. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com