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      lex: "Measured: 0.9993 median R^2 of log(diameter) vs whorl index per specimen, ammonoids (Nautilus 0.9995; gastropods 0.987) (n = 434, specimens: 93 Nautilus, 177 ammonoid species, 164 gastropods; min R^2 0.9984 / 0.9605 / 0.0867). Interpretation: Thompson\'s \'breadths of successive whorls along a radius in geometric progression\' is tested on its equivalent for measured cross-sections: conch diameters at successive half-whorls, whose ratio is constant if and only if the whorl breadths are in geometric progression (both equal e^(pi cot alpha) per half-whorl for a logarithmic spiral). Korn\'s WER = (dm1/dm2)^2 is that half-whorl ratio squared, i.e. the per-revolution ratio Thompson quotes as \'about three\' for Nautilus. The strict reading (a single constant ratio for the whole shell) and the approximate reading (a logarithmic spiral is a very good description) are both pre-registered so that the verdict distinguishes them. Station spacing differs by dataset (Nautilus 45 deg, ammonoids 180 deg, gastropods 180 deg); the fits use the station index, and the per-revolution ratio uses the appropriate lag (8, 2, 2). For gastropods the measured radius is the perpendicular distance of each digitised aperture\'s centroid from the coiling axis (Collins et al. 2021 raw tps data), the quantity Thompson\'s spiral describes for a turbinate shell."
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