With this data set we provide representative and relevant data for the analyses provided in https://arxiv.org/pdf/2512.17716 via HDF5 files, namely at half-filling the values T=1/15t, U=4,5.5,5.9,5.92t, where the latter is the closest data to the MIT Uc_2 available. The file names contain first the method (either CDMFT or the ISOLATED cluster), then the interaction value, the temperature, the doping, the second next neighbor hopping and, finally, the size of the impurity cluster 2x2 follows. Please use the following instructions for accessing the different types of data within the respective files: 1) For scalar quantities such as the chemical potential "mu", the data is provided directly with this key. 2) For two-point fermionic objects such as the Green function "Greens_function", each entry contains two-orbital indices with keys running from 0 to 3 for the 2 times 2 cluster case. Then a key "data_Re" or "data_Im" follows. For example: ['Greens_function']['0']['0']['data_Re'] contains a 1D Matsubara data array for a symmetric frequency grid. 3) Further, the Hedin vertex and the bosonic response functions are split into their channels: "char_ch" and "magn_ch", followed by either "hedin" or "susceptibility"-keys. After two- or three-orbital keys "data_Re" or "data_Im" keys follow, before a respective array. For example: A['char_ch']['hedin'][str(i1)][str(i2)][str(i3)]['data_Re'] contains a 2D Matsubara data array, where the odd number of data is the values corresponding to bosonic frequencies for the positive and negative Matsubara frequencies, and the even number the respective fermionic argument. A['chi4_ph']['up_up'][str(i1)][str(i2)][str(i3)][str(i4)]['data_Re'] etc. contains a 3D Matsubara data array with the generalized impurity susceptibility in the particle-hole frequency notation where the column order represents [omega,nu,nu'] in the convention of the paper, where the given omega=0. The irreducible vertex is stored as A['Gamma_c']['up_up'][str(i1)][str(i2)][str(i3)][str(i4)]['data_Re'] and the lattice charge response on the cell as A['chi4_c_lat']['up_up'][str(i1)][str(i2)][str(i3)][str(i4)]['data_Re'] etc. for q=0. The HDF5 files can, for instance, by access in python via https://www.h5py.org/. If there are any questions left, feel free to get in touch.