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      lex: "Measured: 80.48 degrees, median constant angle of Nautilus pompilius (r = 2.87 per revolution) (n = 93, Nautilus IQR 80.27-80.68 deg (r 2.81-2.94); population medians 80.4 (Indonesia), 80.4 (Malaysia), 80.7 (Philippines)). Interpretation: Thompson defines the constant angle through the per-whorl ratio of radii or whorl breadths, r = e^(2 pi cot alpha), and reads the angle off that ratio; the test therefore measures r and converts it with his own formula rather than fitting tangent angles to outlines. Modern \'whorl expansion rate\' (Korn: WER = (dm1/dm2)^2 across half a whorl; Raup: W per revolution) is the same quantity for a planispiral shell. \'Ordinary ammonitoid shells\' is operationalized as the species in a large published cross-section dataset (Devonian-Jurassic), \'typically spiral gastropods\' as the 25 fossil and modern helicospiral species measured by Collins et al. 2021; neither sample was chosen by the tester. Deviation from the pre-registration: Collins et al. publish no per-revolution W (their W_e is a fitted rate of aperture-area increase), so r was computed directly from their raw digitised apertures (distance of the aperture centroid from the coiling axis at 180-degree steps, r = r[k+2]/r[k]), which is Thompson\'s own quantity; Nautilus r was likewise taken directly as dm[i]/dm[i-8] over the 45-degree stations rather than through WER."
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      lex: "Pre-registered. \'refutes\' if the Nautilus median alpha is outside [76, 84] deg, or if in either the ammonoid or the gastropod sample fewer than 40% of species fall in [80, 85] deg, or more than 20% fall below 80 deg. Anything between the pass and fail thresholds is \'mixed\'. If the gastropod expansion parameter cannot be mapped to a per-revolution ratio from the dataset\'s documentation, part (c) is reported as not operationalizable and the verdict rests on (a) and (b) with a caveat."
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      lex: "Sensitivity (not pre-registered, computed in a side check): the ammonoid in-band fraction is 0.26 with no size threshold, 0.32 at dm >= 5 mm (pre-registered), 0.29 at dm >= 10 mm, 0.26 at dm >= 20 mm, and 0.33 using only each species\' last measured revolution; the median alpha stays at 85.5-85.6 deg and the below-80 fraction at 0 throughout, so the verdict does not depend on the threshold."
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