Geometric parameters to be used throughout the paper according to the ‘observer’s convention’, which is used throughout the text. For the description of the fundamental reference frame (axes in yellow) and the orbital reference frame (axes in blue), see Sect. 2. For the orientation of the pulsar angular momentum, S, and its magnetic axis, μ, relative to this frame, see the detailed explanation in Sect. 3. In this figure, S is represented as being parallel to the direction of the orbital angular momentum, k. This is true for binaries such as PSR J2222−0137, where the pulsar was fully recycled by mass accretion from the companion and the companion then evolved into a WD. If the second-formed object in the system were a NS, then the kick from the supernova event that formed it might substantially change the orientation of the orbit (and thus the orientation of k) relative to S and greatly increase its eccentricity. The figure is by Vivek Venkatraman Krishnan.