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Fig. A.1.

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Galaxy sky density of (proto)cluster cores in comoving area. Densities were measured in a 10″×10″ area with the maximum number of cluster members covered by the area, where we applied a stellar mass limit log(M*/M) > 10.2 for optical-detected members and a flux limit S1mm > 0.3 mJy for 1 mm continuum detections, respectively. We show extreme cases in literature from Wang et al. (2016), Miller et al. (2018), Willis et al. (2020), and Daddi et al. (2021). We note that CL J1001 and DRC lack 1 mm observations; their 1 mm fluxes were derived by scaling their 870 μm and 2 mm continuum under assumption of a GN20 dust template (Magdis et al. 2012). HPC1001 is highlighted in green, showing the highest density at z > 3.

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