We are publishing an update to OpenAI problem #109 Integer multiplication) with another substantial further tightening: κ = 2⁻⁵⁹ (from OpenAI’s original κ = 2⁻¹⁸²) Approximately 500 thousand fold improvement over our previous result and a 2¹²³ fold improvement over the original OAI result. The latest redesigned the finite network to share intermediate computations and scratch space, then tightened the recursion and Gaussian estimates.