## 3 Results and Discussion
### XPS Data Matrix
In fact, the averaged results from the XPS analyses of the four samples considered in Figure 5 and Table 2, so different in appearance, as widely specified, align perfectly with those of the new building at the last sampling (after 52 months), within the limit of the total variability due to sampling, to the calculation of the curve-fitting, as well as to the orientation of the walls and to the characteristics of the samples themselves, the latter expected with greater specificity given the dimensions of the old building and, therefore, of sampling areas with probable different exposure even along the same wall. Principal Component Analysis (PCA) was finally applied to the entire XPS dataset of Table 3, using the R-based version 3.1.2 of the CAT software available online [24], with the aim of evaluating the information content of the variables while reducing their number, eliminating the redundant ones. The matrix includes 22 surface samples of calcarenite collected at the given time intervals, the blank calcarenite 0R, 4 samples of the old building (1v-4v) and 8 variables, i.e., the percentage of the chemical groups listed aside the XPS graphs of Figure 6 plus Ca\({}^{2+}\)/CO\({}_{3}\)\({}^{-}\) binding energies (BEs) known to be sensitive to the calcium carbonate structural changes [25; 26]. The graphical output of the CAT software is shown in Figure 7a-c where the combined display of the three graphs, scree, scores and loading plots helps the interpretation of the data to rationalize the degradation processes under consideration. A scree plot illustrating the distribution of variance among the principal components is provided in Figure 7a, offering visual evidence of component selection. A total variance higher than 80% was explained by PCA, with the two first components PC1 and PC2 able to explain the compositional variation of 'calcarenite' under environmental exposure and extract the main indicators of degradation. Three main clusters were observed in the score plot, distributed along PC1 (63.3% of the explained variance). Samples collected from the new building after 52 months of exposure and from the old building,1v-4v were located on the same side of the plot, thus suggesting the same surface composition of the long-weathered samples. On the opposite side of the score plot, samples collected within 3 and 21 months were present. In detail, two main clusters were observed in this section along PC2 (18.2% of the explained variance): the first, widely distributed, included 0R and the four wall samples collected in the first nine-month time interval, the second actually consisting of two overlapping clusters each made of samples collected from the cubic walls after 12 (red cluster) and 21 (green cluster) months very closely distributed. From the loading plot view, the variables mostly contributing to the first principal component PC1 were detected, i.e., (%Al-silicates, %C-C, %, COx/CN) and (%Ca2+, %CO32-/C2O42-, %M-oxides), which were inferred to be negatively correlated with each other. Thus, by increasing the outdoor exposure, an increased content of aliphatic/aromatic and functionalized carbons of Al and Si (grouped as Al-silicates in Figure 6) could be noticed while decreasing the content of carbonates and mixed-oxides. The PCA plots of Figure 7 overall agree with the XPS plot of Figure 6 and support the interpretation given on the decay trend of calcarenite over time. Moreover, another agreement concerns the BE behavior of Ca2+ and CO3-, the carbonate constituents, considered as additional variables for PCA, mostly contributing to the PC2 component. Viewing the score and loading plots together, it can be seen that their BEs increase with outdoor exposure in the first year.