Collatz Conjecture Endures; Zermelo Problem Solved via Quantum Annealing — E8 Intelligence Research

FINDING: Collatz Conjecture remains the canonical "simple-to-state, impossible-to-prove" problem; Zermelo's navigation problem gains a quantum-annealing solution via Landau-Zener approximation. | MATH: Collatz map: \( T(n) = n/2 \) if \( n \) even, \( T(n) = 3n+1 \) if \( n \) odd; open question: does \( \forall n \in \mathbb{Z}^+ \), \( \exists k \) such that \( T^k(n) = 1 \)? Zermelo: minimize \( \int_0^T \| \dot{x}(t) - \mathbf{v}(x(t),t) \|^2 dt \) subject to \( \dot{x} = \mathbf{u} + \mathbf{v} \), \( \|\mathbf{u}\| \le U_{\max} \); Landau-Zener transition probability \( P = \exp(-\pi \Delta^2 / (2\hbar |\dot{\epsilon}|)) \) — no new constants or ratios emerge from the search results. | CONNECTION: None directly stated. Collatz's \( 3n+1 \) structure has no known link to 0.382, 0.618, 1.618, or base-60; Zermelo's problem is a variational calculus problem — no crystallographic or root-system symmetry appears in the abstracts. | DEPTH: 3 — The Collatz result is a famous open problem Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com