## 3 Results and Discussion
### XPS Data Matrix  
* At% composition resulting from the curve-fitted spectra of the four walls of the cubic building at the reported sampling time, with the exception of the sampling after six months performed only on two walls, N/E, and the four NE samplings of the old building (1v-4v). * The last two columns with the (corrected) BEs for Ca\({}^{2+}\) and CO\({}_{3}\)\({}^{-}\) peaks of the carbonates at each sampling were included as additional variables for PCA to verify the BE chemical shifts versus reference calcarenite 0R as a function of time. Figure 6 shows the completed S2b plot using, of all the curve-fitted data reported in Table 3, the average of the same chemical groups (XPS indicators of degradation, listed in the legend) present on the four walls of the new building at each sampling time and, similarly, the average of the four samples collected from the walls of the old building (old farm). As anticipated, the decay trend based on the Figure S2b option seems more justified with the increasing time, in particular, for the new building, given its small size. Therefore, the contributions averaged on all oriented faces are more appropriate, and the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Name.** & **Times** & **C-C** & **COx/CN** & **Carbonate/** & **Ca2* & **M-Oxides** & **Al-** & **BE C1s** & **BE** \\
**Samples** & **Sampling** & & & & & & & & \\  
\end{tabular} The sample codes, referred to in the newly installed calcarenite cube, combine the sampling time in months with cardinal orientations: the letters ”N, E, S and O’ indicate samples collected from the north-, east-, south- and west-facing walls, respectively, while the letter ‘v’ refers to the old farmhouse.  
\end{table} 
Table 3: Data matrix representing the entire collection of XPS results from the periodical monitoring of the new cubic building to the old farm. balance of their hydration/dehydration percentage observed in the nine-months interval better justifies the omission of the total oxygen area as a 'decay indicator' being implicitly accounted for by the total contribution of oxygenated compounds, verifiable a priori during the curve-fitting procedure. The sampling variability across the four walls, shown by the 'error bar' of each decay indicator in Figure 6, is represented by the standard deviation associated with the mean value of the four collected samples. Instead, as said and shown in Figure S1 for single samplings, the uncertainty associated with the reference sample 0R is to be considered equal to \(+/-10\%\)[19,20] and therefore doubled in the case of only two samples collected at 6 months. The compositional changes already observed after three months are progressing, maintaining the trend over the course of the first year of exposure, with the variability ranges reflected in the magnitude of the standard deviations associated with the means. The percentage variations are clearly linked to the different contribution of the individual walls, evident in Figure S1a-d classified by cardinal orientation. In Figure 6, the influence of meteorological fluctuations and washing away of the wall surfaces by precipitation with the consequent removal of the crystallized salts present on the surfaces ('extra cations/anions' in the graphs) and other reasonable differences in the composition of the sampling zones are all included in the variability associated with the 'averaged' indicators of samples collected from different walls/areas of the cubic building. After the first year, sampling was no longer scheduled every three months; however, at the end of the year, after the 12 months of sampling, the imbalance of the carbonate components tended to be reduced, then reached with the sampling at 21 months.