Collatz Conjecture: The Unproven Frontier in Machine-Solvable Math Problems — E8 Intelligence Research

FINDING: The Collatz Conjecture remains the canonical "simple-to-state, unproven" problem in live competition discourse; the MATH dataset quantifies the frontier of machine-solvable competition problems. | MATH: Collatz map: \( T(n) = n/2 \) if \( n \) even, \( T(n) = 3n+1 \) if \( n \) odd; conjecture: \( \forall n \in \mathbb{N}, \exists k: T^k(n) = 1 \). No closed-form solution; known statistical behavior: average growth factor per step \( \approx (1/2)^{1/2} \cdot (3/2)^{1/2} = \sqrt{3/4} \approx 0.866 \), implying logarithmic drift toward 1. MATH dataset: 12,500 problems, 7 subjects, 5 difficulty levels; no inherent constants beyond problem structure. | CONNECTION: The Collatz map's parity-based branching is a binary tree structure — a 1D lattice with self-similar scaling. The expected multiplicative factor \( \sqrt{3/4} \) is not a golden-ratio harmonic, but the orbit lengths show log-normal distributions with variance related to \( \ln(3/2) / \ln(2) \) — a ratio \( \approx 0.585 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com