The uploaded files contain structures and ids for ~2M compounds from AFLOW-LIB (~900k), the materials project (~100k) and our own group (~1M). 
The data was obtained by collecting all calculations with compatible parameters and removing duplicates (details in the paper).
For the AFLOW-LIB and materials project data the structures and energies can be downloaded using the provided IDs.
For our data we directly provide the relaxed structures and energies.
The computed_entries.tar.gz contains all data from our group except the mixed perovskites that were predicted that can be found in 
predicted_mixed_perovskites_computed_entries.tar.gz

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To read computed_entries.tar.gz in python uncompress it and (same for predicted_mixed_perovskites_computed_entries.tar.gz):
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#!/usr/bin/env python

import json
from pymatgen.entries.computed_entries import ComputedStructureEntry

data = json.load(open('computed_structure_entries.json','r')) 


entries = [ComputedStructureEntry.from_dict(i) for i in data]

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The Id files can be loaded in the same manner in python

import json
data = json.load(open('..','r'))

but directly provide a python dictionary with the four keys
'id', 'd_e_hull', 'e-form', 'spg'.
The dictionary entries contain lists with the corresponding values.