The distance-seven containment conjecture for the Pyro game

Consider the Pyro game on the infinite Cartesian grid, with the original burned vertex at $(0,0)$ and one firefighter protecting vertices over successive steps. Here, a vertex's distance is its graph distance from $(0,0)$. Distance-seven containment conjecture. One firefighter can prevent the pyro from burning any vertex distance $7$ from the original burned vertex $(0,0)$ on the infinite Cartesian grid. The paper says that the authors claim to have a proof, but that it is unpublished because of its length and that a more clever proof is hoped for; thus the claim is treated as open in the database.