Collatz Conjecture and Quantum Navigation: Unifying Simple Unsolved Problems — E8 Intelligence Research

Abstract

FINDING: Survey of "impossible" problems reveals Collatz Conjecture as the canonical simple-yet-unsolved case, with Zermelo's navigation problem newly solvable via quantum annealing/Landau-Zener approximation. | MATH: Collatz: T(n) = n/2 if n even, 3n+1 if n odd; conjectured to reach 1 for all n ∈ ℕ. Zermelo: optimal control of vessel in flow field, Hamiltonian H(t) with Landau-Zener transition probability P = exp(−πΔ²/(2ℏ|dE/dt|)). | CONNECTION: Collatz's 3n+1 operation encodes a discrete dynamical system with no known invariant — but its parity structure hints at a 2-adic (base-2) lattice, not base-60. Zermelo's solution via quantum annealing maps to a spin-glass energy landscape, whose ground states often exhibit crystallographic symmetry breaking — but no explicit 0.382/0.618/0.786 ratio appears in the provided abstracts. | DEPTH: 4 — The findings are a curated list, not a breakthrough. The Zermelo result is the only novel mathematical advance, and its connection to geometric harmo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com