We present computational evidence supporting the following conjecture: w(2;4,4) = 35: every 2-coloring of {1,...,35} contains a monochromatic arithmetic progression of length 4. Verify computationally by showing all 2-colorings of {1,...,34} avoid monochromatic AP-4 (proving w > 34), and {1,...,35} does not.. An exhaustive search over 35 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.