*Meta-analytic data thresholding and parcellation*

Brain functions were derived from the open-access Neurosynth22 database, an automated platform that computes whole-brain meta-analytic activation maps for specific cognitive terms. The meta-analytic maps indicate the strength of the activations associated with a specific term as a z-score for each brain voxel. The meta-analytic dataset used in the present study includes 506 functions representative of the state-of-the-art in the exploration of the anatomy of brain cognition from 1997 to 2017 (11406 literature sources) that were manually curated and validated in a previous study41. To allow for the replication of the quantitative relationship between the maps (see Supplementary Materials), only the meta-analytic activation maps that were also available in the 2021 Neurosynth collection were selected. 84 meta-analytic maps missing from the 2021 collection were excluded from the original dataset of41.

The 506 meta-analytic maps (Neurosynth 2017) were thresholded at z=3.4 (p=0.000337) to ensure the generalisability of the brain-cognition architecture to recent meta-analytic data. Neurosynth applies a threshold of z=3.4 to meta-analytic maps obtained after 2017 to correct for multiple comparisons.

Each map underwent a comprehensive cortical (MMP,23) and subcortical (AAL3,24,25) parcellation. We thus obtained a total of 440 brain parcels per meta-analytic map and extracted mean z scores for each parcel.

The thresholding and parcellation were applied in FSL (fslmaths and fslstats respectively, https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSL).

*Brain-cognition space embedding*

The Uniform Manifold Approximation and Projection (UMAP,26) algorithm was used to reduce the dimensionality of the parcelled meta-analytic dataset in a two-dimensional embedding space.

UMAP is a non-linear low-dimension projection technique that learns the manifold structure of data while retaining its core organisation in a lower dimensionality embedding26. UMAP was applied using the eponymous UMAP Python library (umap-learn.readthedocs.io) with default parameters. Specifically, the space was built in two dimensions to foster the interpretability and successive manipulation of the data organisation; the algorithm used the information of 15 local neighbours to learn the manifold structure of the data points; 0.1 minimum distance was allowed by the algorithm to pack the data; the Euclidean metric was used for the data embedding. In the embedding, maps with similar activation patterns clustered together, while different maps spread apart. The Python library Pickle stored the embedded transformation of the meta-analytic dataset as a Python object, allowing the dimensionality reduction and projection of external data in the same embedded space (https://github.com/vale-pak/BCS/tree/BCS_computation).

*Rationality index computation *

The spatial relationship between meta-analytic activation maps was exploited to test the predictability of the anatomy of each of the functions and obtain a novel index that we will address as a rationality index because it has the property to summarise the embedding space underlying the organisation.

The linear spatial relationship among the maps was computed as the shortest distances (Euclidean distances) between the maps embedded in the BCS. The pattern of activation predicted for each map was obtained by voxel-wise linear regressions in FSL’s (https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/Randomise/UserGuide) randomise where the distances were set as dependent variables, and the 505 maps used to build the BCS (506 - 1 to-be-predicted map) as independent variables. Since the resulting t-stat maps underwent further transformation and thresholding, no permutation was applied to correct for multiple comparisons during the linear regressions. Hence, the 506 t-maps were transformed into z-maps and thresholded at a z=3.4 to allow for the comparison with the measured meta-analytic maps. The rationality index was computed as Pearson's R using fslcc in FSL (https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/Fslutils), comparing each measured meta-analytic map to the corresponding predicted z-map.

*Rationality index laterality*

The parcels of the 506 predicted maps were divided into left and right hemispheres parcels, and the mean z-statistic of left and right structures was computed for each predicted functional map. Then, the t-test comparison was conducted in JASP (https://jasp-stats.org/) to explore the mean rationality index differences between the left and right hemispheres.

*Rationality map computation and correlation with activation gradients*

The rationality index computed for each of the 506 meta-analytic maps was used as an independent variable in a linear regression with the measured maps as dependent variables via randomise tool of FSL (https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSL/randomise). The regression allowed the identification of structures associated with high rationality index. To test whether the rationality pattern of this map corresponded to a typical gradient activation, Pearson's correlations were computed between the obtained rationality map and each of the five activation gradients21.

*Embedding transformation and prediction of new functions*

New, undescribed meta-analytic and raw-data functional activation maps were used for testing the new functions' prediction power of the BCS (https://github.com/vale-pak/BCS/tree/New_maps_projection).

Thirteen new cognitive terms and corresponding meta-analytic maps that were not included in the 2017 dataset were retrieved from the 2021 version of Neurosynth (14371 literature sources). The same exclusion criteria applied for the selection of 2017 maps were used41. Briefly, terms referring to studies on neurodevelopmental and brain disorders were not taken into account.

The selection of raw functional activation maps of new studies (i.e. published after 2017) was conducted on Neurovault (https://neurovault.org/). We scrutinised the repository for task-related activation maps of studies published after 2017 using the branches' cognitive domains or the functions with the highest rationality index as keywords. Studies involving psychiatric and pathological populations were not considered. Nineteen new activation maps were selected. When necessary t-stat maps were transformed into z-maps, registered to the MNI152 and thresholded at z=3.4.

All the test data maps (the new meta-analytic and raw activations datasets) underwent the same parcellation as the 2017 maps. Then, UMAP allowed for the two-dimension embedding of the new test data based on the previously defined BCS embedding. Coordinates of the locations of each new map were extracted in the BCS space.

The Euclidean distances between each new map and the 506 BCS-measured maps were exploited as the dependent variable in the linear regressions to predict the anatomy of the new maps. The t-stat maps resulting from the linear regressions were transformed into z-maps, thresholded at z=3.4, and parcellated. The rationality index between the measured and predicted test data were computed using Spearman's correlations.