Nonextendibility of symmetric one-dependent four-color laws to a branched ray

Let a graph consist of a root, two leaves adjacent to it, and an infinite ray starting at the root. We prove that this graph admits no color-symmetric, one-dependent proper four-coloring whose law on every ordered simple path agrees with a common stationary, reflection-invariant line law. The line law is arbitrary. An infinite color-avoidance recurrence bounds every specified one-step extension by half the probability of its prefix. Together with finite marginal identities, this gives an exact rational contradiction. The finite calculation is computer-assisted; a complete certificate and a verifier using only rational arithmetic are supplied.