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This is necessary reading to understand Purifi's design choices. In a nutshell - the annulus (the surround) is the most nonlinear component of the radiating surface, and is the source of the majority of a driver's second-order distortion (2nd harmonic distortion combined with first sum and difference tones). Consequently, the T/S parameter corresponding to the radiating area, the Sd, doesn't remain constant, even though speaker designs tend to ignore that fact and assume it to be constant. It is also why larger cones with shorter excursions have less distortion than small cones with large excursions: more consistent Sd.
Purifi calls attention to this oversight and has taken measures to reduce the problem, hence the distinct annulus. It enables them to have very large excursions without sacrificing reliable performance. Secondly, the wavy shape mitigates the torque the in-and-out surround would have otherwise caused on the cone.