10 · Turn the dial

Every constant in the paper, as the dial (the bandwidth) turns and the window switches.

Try this. Pull the dial to one and watch all three certificates peak: two thirds on the line and clean, five sixths distinct. Then switch to the optimised window for the last half percent.

The curves are the paper's shape functions, computed live; the optimised-window constants come from the closed form the paper states, which the tests pin to 0.67250 and 0.83625. The dial cannot pass one: beyond it the prime sums would need knowledge nobody has.