8 · Stretch until the two agree

A certificate and its Fourier transform. The slider stretches the certificate.

Try this. Find the stretch where the two curves meet at the centre. That is the only stretch for which subtracting them gives a function that is zero there, and the whole rest of the proof needs it.

The exact stretch is the ratio of the two values at the centre, taken to the power one over the dimension. Here that is about 0.75, and the page recomputes it rather than assuming it.