A Chladni figure is not a picture of vibration. It is a picture of the places that refuse to vibrate. Draw a bow across the edge of a metal plate and the sand does not gather where the energy is — it flees there. It settles along the nodal lines, the curves where the standing wave cancels itself and the plate is perfectly still.
Which is a reasonable description of how a number gets fixed. Not by being asserted more loudly in more places, but by being the one value the numerics stop arguing about. r★ = 0.77594058 is where the integrator falls silent. Everything else was amplitude.
The inner boundary is asymmetric: Grönwall gives the symmetric ball |r−1| < 1/3, and the flow does not respect it. The certified edge sits at 0.77594058, not at 2/3. The gap between the estimate and the truth is not an error to be embarrassed by — it is the whole pedagogical content of the course.