math-017-prove: Prove The Littlewood Conjecture

[IndieMath:math-017:prove] Prove the The Littlewood Conjecture conjecture through an IndieMath AI research attempt. Canonical statement: For all real α, β: lim inf_{n→∞} n · ‖nα‖ · ‖nβ‖ = 0, where ‖·‖ is distance to the nearest integer. Contributions fund model usage and related compute for this direction.