The four-colour Rado number of 2(x-y)=3z is 226: a cube-and-conquer computation with checked DRAT proofs

For a linear equation E, the Rado number R_k(E) is the least n such that every k-colouring of {1,...,n} contains a monochromatic solution of E. We show that R_4(2(x-y)=3z) = 226. The lower bound is an explicit 4-colouring of {1,...,225} verified by an independent checker. The upper bound is a cube-and-conquer proof with 14,162 cubes, each re-solved with CaDiCaL and its DRAT proof accepted by drat-trim (14,162 of 14,162 verified). Code, logs and the colouring are public. Not peer reviewed. The literature check was not exhaustive; if the value is already known, this note should be read as an independent verification. Developed with the help of an AI assistant (Claude, Anthropic); the author is responsible for the content.