dataesr/scientific-paragraphs-categorization huggingface dataset:
(2011)  for a detailed explanation). 3) We only include sediment-derived datasets whereby the paleopole and statistical parameters were calculated from a collection of paleomagnetic directions that approximately represent independent readings of the past geomagnetic field, and whereby these directions were corrected for potential inclination shallowing. To select such datasets, we use the reliability criteria formulated by  Vaes et al. (2021) , which assess under which conditions sedimentary datasets may be reliably corrected for inclination shallowing by the E/I correction, while satisfying the underlying assumption of that method that each of the paleomagnetic directions may be considered an independent reading of the past geomagnetic field. We only include E/I-corrected sedimentary datasets that would receive a grade 'A' or 'B' according to the evaluation scheme of  Vaes et al.
(2021). In addition, we have included two datasets that satisfy these criteria but were corrected for inclination shallowing using an anisotropy-based approach  (Kodama, 2009; Brandt et al. , 2019). We note that these criteria for sedimentary rocks are far more stringent than in previous compilations for the computation of APWPs, and only 29 sediment-derived datasets are used in the computation of the global APWP. 4) As a final selection criterion, we only include datasets with an age uncertainty range of <20 Ma: datasets with larger age uncertainties would lead to needless smoothing of the global APWP.
Results We computed a global APWP for the last 320 Ma using a 10 Ma time interval and a 20 Ma sliding window. The APWP is based on a total of 13,737 simulated VGPs that are derived from 350 different paleomagnetic datasets (Table  2 ), yielding a mean and median number of sites per dataset of ~39 and 19, respectively. Of these datasets, 162 were included in the compilation of  Torsvik et al. (2012) , 71 in the PSV10 database  (Cromwell et al. , 2018)  and 117 were added during our data compilation (most of which were published post-2011). The new global APWP is shown in Fig. 5  as reference poles per 10 Ma that are plotted as south poles in South African coordinates (see also Table  3 ). The global APWP in the coordinate frame of other major tectonic plates, including North America, South America, Eurasia, India, Australia, Antarctica and the Pacific is given in Table  4.
7 • ) (Table  3 ). The reference poles of the APWP are computed from, on average, 813 parametrically simulated VGPs. The lowest data density is observed for the Late Jurassic, with only ~110-150 sites per time window. As expected, the highest data density is obtained for the last 10 Ma, provided by the large number of sites included in the PSV10 dataset. Additionally, the early Cenozoic (50-60 Ma) and Late Triassic (200-220 Ma) segments of the APWP are also based on large datasets of simulated VGPs. For each time window, we computed the mean values of the Fisher precision parameter (K), the circular standard deviation (CSD) and elongation (E) for each iteration from the distribution of simulated VGPs that were included in that window (Table  3 , Fig. 6b ). The values for K are on average 20.
6 • /Ma or lower. There seems to be no clear correlation between the APW rate and age, and age bins with relatively low APW rates alternate with slightly faster APW throughout the studied time span of the pole path. On the other hand, the observed APW rates and position of the reference poles may be influenced by an uneven temporal distribution of the simulated VGPs. For example, a large dataset with relatively tight age constraints may 'pull' a reference pole towards the paleopole with large N. This temporal bias may be identified from a relatively large difference between the center age of the window and the mean age of the simulated VGPs that fall within that time window (see Fig. 6c ). For example, the high APW rate between 230 and 240 Ma may be explained by the difference in mean age of the simulated VGPs of ~18 Ma.
Besse and Courtillot (2002)  suspected that because some degree of deformation is often necessary for rocks to be exposed at the surface, unrecognized local deformation (such as local rotations caused by plunging fold axes) may be an important source of noise in APWPs. In the conventional approach in which each paleopole is assigned equal weight, the bias resulting from a single dataset that is affected by one or more of the above artifacts is unlikely to be large. However, if such a dataset has a large number of sites, its relatively large weight may cause considerable bias in the APWP calculated from sitelevel data. We first evaluate the influence of large datasets on the global APWP by parametrically re-sampling only 50 VGPs for all paleomagnetic datasets that are based on >50 sites. The resulting APWP is very similar to the one presented in the previous section (Fig.
7 ). As expected, the confidence regions for many reference poles are larger, as they are based on fewer sites. We observe two main differences. First, we observe that the reference poles with time windows centered at 50 and 70 Ma are at a larger angular distance from the 60 Ma reference pole, as they are pulled less towards the larger number of simulated VGPs derived from paleopoles with ages of ~60 Ma. Second, the 240-300 Ma segment of the APWP becomes a smoother path. This shows that although no major differences are observed, large datasets indeed alter some segments of the APWP. However, since we do not know the 'true' APWP, it is difficult to assess whether the influence of a large datasets represents a bias in the Table  3  Global APWP for the last 320 Ma in South African coordinates, calculated using a 20 Ma window.
, 2020). Even though these dispersion values are not obtained from real VGP-level data, we hypothesize that this lower dispersion may reflect a suppression in the magnitude of PSV during these intervals with stable magnetic field polarity, as was previously proposed (e. g. ,  Brandt et al. , 2019; Handford et al. , 2021). We note, however, that the lowest dispersion of simulated VGPs is observed for the age windows centered at 130 and 140 Ma, whereby the majority of the input data is derived from large igneous datasets of South America and southern African that are associated with the Parana-Etendeka LIP. This low dispersion of simulated VGPs may be explained by the fact that the data is obtained from rocks of a relatively short age interval and is likely less affected by noise resulting from unrecognized local deformation or plate In summary, the statistical parameters obtained for the global APWP indicate that the dispersion of simulated VGPs used to compute the APWP is similar to that what would be expected from PSV alone.
This shows that the errors that undoubtedly exist in our dataset due to e. g. , unresolved overprints, unrecognized tectonic deformation, plate circuit errors, or age errors, do not form a major contribution to the scatter of the simulated VGPs that fall within the same time window, which would drive the dispersion beyond values that typically represent PSV and/or lead to an elongation of the distribution of simulated VGPs. This suggests that the global APWP presented here is robust and that it represents the time-averaged paleomagnetic field for each interval.
9 • and 4. 1 • , respectively. These APWPs were all computed using the same running mean approach with a time step of 10 Ma and a sliding window of 20 Ma, and the observed differences thus resulted from differences between the compilations of paleopoles and plate reconstruction parameters. But even though we constructed our path using (i) simulated VGPs instead of paleopoles, (ii) an updated paleomagnetic database obtained with more stringent selection criteria and (iii) an updated global plate circuit, we obtain a path that is, to firstorder, similar to the most recent pole-based APWP of Torsvik et al. (2012) (see Fig. 5a ). This clearly shows that the overall geometry of the path is well-constrained, and strengthens confidence that paleomagnetism provides a reliable and reproducible reference frame as basis for paleogeography and paleoclimate for the last 320 Ma.
The increase in independent data points thus outweighs the larger dispersion of simulated VGPs (with a K of ~15-35) compared to that of coeval paleopoles (with K values of ~100, see  Rowley, 2019; Vaes et al. , 2022). The smaller confidence regions obtained from using site-level data instead of paleopoles was previously observed for the PSV10 dataset by  Vaes et al. (2022). This suggests that the resolution and precision obtained with paleomagnetic data has long been underestimated by artificially decreasing the number of data points underlying APWPs due to the averaging of arbitrarily defined collections of sites into paleopoles. Although the first-order geometry of our new global APWP is similar to that of  Torsvik et al. (2012) , there are several time intervals for which there are notable differences.
For instance, the reference poles of the 30-40, 90-100 and 310-320 Ma segments of the path, as well as the poles at 200 and 230 Ma, are at an angular distance of >3 • (Fig. 8a ). We interpret these differences as being mainly caused by our site-level approach and the updated paleomagnetic database, to which we added recently published data but from which we also excluded many paleomagnetic datasets due to the application of our more stringent selection criteria. In addition, we note that differences in the effective The largest difference between our new global APWP and that of  Torsvik et al. (2012)  is observed for the 140-170 Ma segment, yielding an angular difference of ~4• (Fig. 5, 8a ). This segment of the APWP of  Torsvik et al. (2012)  was based on relatively few paleopoles (<20 per time window), and the observed differences may partly be explained by the inclusion of recently published datasets in our database, e.
g. , (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. )  Domeier et al. , 2012 Domeier et al. , , 2021;; Gallo et al. , 2017; Kent and Muttoni, 2020, Kent et al. , 2021; Pastor-Galán, 2022) , or the 'east Asian inclination anomaly' in the Paleogene (e. g. ,  Cogné et al. , 2013). The observed mismatches between paleomagnetic data and APWPs of different continents and tectonic plates have generally been based on analyses using pole-level data. These discrepancies may be re-evaluated using a sitelevel approach, in which spatial and temporal uncertainties are explicitly incorporated, which have often been omitted in comparative analyses. Evaluating whether previously inferred anomalies still exist when using our site-level approach requires a detailed review of the underlying data, which is beyond the scope of this paper.
g. ,  DeMets and Merkouriev, 2021). We foresee that the propagation of these errors will provide only marginal gains. Second, a statistical framework for the full propagation of the errors through the hierarchical levels of paleomagnetic data, that is from the individual demagnetization steps to the VGP or paleopole -has yet to be developed. Recent advances in the statistical treatments of paleomagnetic data  (Heslop and Roberts, 2016, 2020)  or directional statistics (e. g. ,  Scealy et al. , 2022)  may provide promising avenues for improved propagation of these fundamental uncertainties behind paleomagnetic data. Ideally, future APWPs could be computed from real site-level data rather than from simulated VGPs (e. g. ,  Gallo et al. , 2023). Such an approach would avoid the necessity of adopting a pre-defined distribution of VGPs, such as the assumed Fisher distribution used here, which is a useful but not entirely accurate approximation of the distribution of VGPs (e.
g. ,  Tauxe and Kent, 2004; Deenen et al. , 2011). When using a parametric re-sampling approach, the Fisher distribution is essentially the only option, however, for the simple reason that statistical parameters describing the paleomagnetic data distributions have traditionally been reported in the framework of  Fisher (1953). An important advantage of using the published site-level data is that it allows the systematic application of selection criteria and data filters on the site-level. Building the database from the real VGPs would also enable the propagation of age uncertainties that are defined at the site level, provided by numerical age determinations of individual sites as well as by relative temporal relationships between sites  (Gallo et al. , 2023). Temporal biases in VGP-based APWPs, caused by an uneven distribution of VGP ages, may then be mitigated by assigning more weight to sites that have an age closer to the center age of the moving time window, as recently proposed by  Gallo et al.
(2023). Apart from the fact that not all site-level data is available for the studies included in the data compilations that underlie global APWPs, the compilation of more than ten thousand sites from hundreds of publications would require an enormous effort. Whether the calculation of a global APWP from the published VGPs would yield different results from our re-sampling approach remains to be investigated. To enable the computation of VGP-based APWPs in the future, we strongly recommend paleomagnetists to archive their published data at the site, sample, and measurement level, e. g. , in the MagIC database  (Jarboe et al. , 2012)  or the Paleomagnetism. org data library  (Koymans et al. , 2020). We emphasize that the calculation of a reference APWP from sitelevel data provides opportunities to significantly improve intervals of the global APWP by collecting large datasets of independent readings of the past geomagnetic field (e.
g. , from thick sequences of lava flows or sedimentary rocks), particularly for time intervals that have a relative low data coverage. Moreover,  Dupont-Nivet et al. (2010)  already argued that the precision and temporal resolution of reference APWPs provides a limiting factor in the analysis of detailed tectonic problems, such as the estimation of convergence rates between tectonic terranes that are not included in a plate circuit. They therefore tried to stimulate the paleomagnetic community to focus part of their efforts on collecting datasets from stable plate interiors that may improve the accuracy and precision of the global APWP. We suggest here that rock formations that have provided reliable paleomagnetic data in the past but that include, as of yet, only a relatively limited number of sites may provide particularly useful sampling locations for this purpose.
In addition, we highlight that our new approach allows the comparison of independent paleomagnetic datasets against the global APWP at the site-level, which may improve the robustness of future determinations of relative tectonic displacements such as paleolatitudinal motions and vertical-axis rotations (see  Vaes et al. , 2022). Finally, we note the site-level approach holds great promise to optimize the resolution of APWPs for key time intervals, such as those containing mass extinctions or climate crises: collecting data from such well-dated intervals allows computing a highresolution paleomagnetic reference frame that may be used as input for detailed studies of such events. We foresee that the continuous improvement of the global APWP, both in terms of data coverage and uncertainty incorporation, will enable Earth Scientists to place better quantitative constraints on, for instance, orogenic evolution, the rate and magnitude of TPW, plate tectonic reconstructions and the paleogeographical influence on paleoclimate, paleoenvironment and paleobiology.
Conclusions In this study, we presented a global apparent polar wander path for the last 320 Ma calculated from simulated site-level paleomagnetic data, using an updated paleomagnetic database and relative plate motion model. Based on our new APWP, we conclude the following: • A parametric re-sampling approach allows the straightforward incorporation of both spatial and temporal uncertainties in the paleomagnetic data, as well as uncertainty in the widely used E/I correction for inclination shallowing. Even though these uncertainties are taken into account in our approach, the 95% confidence regions of the site-level APWP are smaller than that of previously computed global APWPs because the much larger number of simulated VGPs per time window compared to the number of paleopoles in the conventional approach outweighs the larger dispersion of simulated VGPs compared to paleopoles.
• The distributions of simulated VGPs that fall within a given age bin resemble the dispersion of VGPs expected for normal geomagnetic field behavior (that is, PSV) in the last few hundred Ma. We interpret this as that there are no major sources of noise that significantly enhance the dispersion beyond expected values for PSV and that would bias the global APWP. • The first-order geometry of the new global APWP is similar to the most recent pole-based APWP of  Torsvik et al. (2012) , with an average angular difference of 2. 8 • between the reference poles computed for the same time window. The average APW rate for South Africa is 0. 38 • ± 0. 23 • (1σ), slightly lower than the 0. 43 • ± 0. 22 • obtained by  Torsvik et al. (2012). The similarity between the previous pole-based global APWP and our APWP computed from simulated site-level data, using more stringent selection criteria, an updated database and global plate model, indicates that the global APWP is robust and reproducible.
• Peaks in APW rate may result from a temporal bias in paleomagnetic data. By correcting for the mean age of the simulated VGPs that underlie each reference pole, we observe that previously identified spikes in APW rate (for South Africa) disappear, while a new peak in APW rate is identified between 100 and 80 Ma. • The calculation of the global APWP at a higher resolution using a time step of 5 Ma and a sliding window of 10 Ma results in a more irregular path with time intervals that show standstills that alternate with segments with relatively high APW rates. We find that the data coverage is certainly high enough to compute a reliable path at this resolution for some time intervals, but not for the entire 320-0 time period. • Calculating APWPs from site-level data provides opportunities to significantly improve the temporal resolution and quality of the global APWP by collecting large high-quality paleomagnetic datasets from stable plate interiors, particularly from rocks derived from age intervals and/or tectonic plates that are underrepresented in the current database.
Acknowledgements BV, DJJvH,  SHAvdL , EvdW, NL, and  AQ  acknowledge  NWO Vici  grant  865. 17. 001  to DJJvH. LCG has received funding from the  European Union 's  Horizon 2020 research and innovation program  under the  Marie Skłodowska-Curie  grant agreement No. 101025975. LMB acknowledges  NWO Veni  grant  212. 247. We thank  Nick Swanson-Hysell  and an anonymous reviewer for their constructive feedback and helpful suggestions. We also thank  Hayfaa Abdul Aziz ,  Hemmo Abels ,  Mohamed Amenna ,  Daniele Brandt ,  Luca Foresi ,  Miguel Garcés ,  Peter Giles ,  Andrey Guzhikov ,  Mark Hounslow ,  Paula Iglesia-Llanos ,  Dennis Kent ,  Maud Meijers ,  Florencia Milanese ,  Vladimir Pavlov , and  Vicente Carlos Ruiz-Martinez  for providing the sample-level paleomagnetic directions that we needed for the application of the E/I correction for inclination shallowing.
Data availability No new paleomagnetic and marine magnetic anomaly data is used in this study. The paleomagnetic data compilation includes datasets from previously published peer-reviewed articles and builds on compilations by  Torsvik et al. (2012)  and  Cromwell et al. (2018). The complete database can be found in Table  S2. The global plate circuit presented in this study consists of previously published Euler rotation poles that are provided in Table  S1. The calculations and analyses performed here benefitted from the functions of the freely available PmagPy software package  (Tauxe et al. , 2016). The Python codes used for the computation of the global APWP, its statistical parameters and the associated figures are publicly available on Github (https://https://github. com/bramvaes/GlobalAPWP) and archived on Zenodo (https://doi.
The human brain data comes from the BigBrain Project (https://bigbrainproject. org) led by teams from Forschungszentrum Jülich and McGill University  (Amunts et al. , 2013). The rhesus macaque data is part of the BrainMaps project (http://brainmaps. org) by Edward G Jones at UC Davis (Figure  1  and Supplementary file 1 for a detailed list). We used our Web tool MicroDraw to visualise and segment the histological data online (https:// microdraw. pasteur. fr). We downloaded the Brain Museum data, and used the vips library (https:// www. libvips. org) to convert it to deep zoom image format -the multi-scale image format required by MicroDraw. The data from the BigBrain and BrainMaps projects is already encoded in multi-scale The resolution of the histological images in the Brain Museum was very variable.
We considered that image resolution was in all cases sufficient to estimate the length and area of the cerebellum sections, however, we excluded some species from our estimation of molecular layer thickness when resolution was deemed insufficient. For this, we plotted the total number of pixels of the image versus cerebellum size, and excluded species where the density of pixels per mm 2 was lower than 3. 5 -a threshold determined by visual inspection. The datasets from the BrainMaps (rhesus macaque), and the BigBrain project (human) were all high resolution (1-20 µm).
Measurement of section area and length of the cerebral and cerebellar cortex Table  1  summarises the variables used in our analyses and their sources. We used the Python package microdraw. py (https://github. com/neuroanatomy/microdraw. py;  Heuer et al. , 2023)  to query Micro-Draw's API and programmatically download all vectorial segmentations and images. We computed the length of the cerebral and cerebellar segmentation contours, and used the scale bar information to convert the data to millimetres. We used an artificial calibration image to ensure that our algorithms produce the correct measurements. Measurements were not modified to account for shrinkage, and reflect the raw data obtained from the images (see  Ashwell, 2020 , for a discussion of shrinkage in the Brain Museum collection).
We measured the width of each folium as the Euclidean distance between its two flanking sulci (Figure  3b ). We measured the perimeter of each folium as the distance along the cerebellar surface between its two flanking sulci (Figure  3c ). For each species we used the median width and the median perimeter across all folia, to make our estimations robust to outliers. The code for computing folial width and perimeter is provided in the accompanying GitHub repository.
Measurement of molecular layer thickness We estimated the thickness of the molecular layer automatically (Figure  4 ). We processed the histological images to convert them to grey levels, denoise them, and equalise their histograms, using functions from the Scikit-image package  (van der Walt et al. , 2014). Starting from the manual segmentation (blue line in Figure  4a ), we created a binary mask and masked out the non-cerebellar Table  1. Definition of the variables used in the current study and their sources.