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We use sub-arcsecond resolution ($\sim$0.4$''$) observations with NOEMA at1.37 mm to study the dust emission and molecular gas of 18 high-massstar-forming regions. We combine the derived physical and chemical propertiesof individual cores in these regions to estimate their ages. The temperaturestructure of these regions are determined by fitting H2CO and CH3CN lineemission. The density profiles are inferred from the 1.37 mm continuumvisibilities. The column densities of 11 different species are determined byfitting the emission lines with XCLASS. Within the 18 observed regions, weidentify 22 individual cores with associated 1.37 mm continuum emission andwith a radially decreasing temperature profile. We find an average temperaturepower-law index of q = 0.4$\pm$0.1 and an average density power-law index of p= 2.0$\pm$0.2 on scales on the order of several 1 000 au. Comparing theseresults with values of p derived in the literature suggest that the densityprofiles remain unchanged from clump to core scales. The column densitiesrelative to N(C18O) between pairs of dense gas tracers show tight correlations.We apply the physical-chemical model MUSCLE to the derived column densities ofeach core and find a mean chemical age of $\sim$60 000 yrs and an age spread of20 000-100 000 yrs. With this paper we release all data products of the COREproject available at https://www.mpia.de/core. The CORE sample reveals wellconstrained density and temperature power-law distributions. Furthermore, wecharacterize a large variety in molecular richness that can be explained by anage spread confirmed by our physical-chemical modeling. The hot molecular coresshow the most emission lines, but we also find evolved cores at an evolutionarystage, in which most molecules are destroyed and thus the spectra appearline-poor again.

The physical and chemical structure of high-mass star-forming regions. Unraveling chemical complexity with the NOEMA large program "CORE"