## 3 Results and Discussion  
The most important advantage of the HR-MAS technique compared to the solid-state NMR is the possibility to obtain well-resolved NMR spectra [40]. Both \({}^{1}\)H and \({}^{13}\)C NMR spectra can be obtained with a spectral quality similar to the liquid state. However, since the organic waste is a complex system, the \({}^{1}\)H HR-MAS NMR spectra are quite complex, due to the overlapping of the signals of the various compounds, and, therefore, for our investigations, the \({}^{13}\)C spectra have been used. A typical \({}^{13}\)C-\({}^{[1}\)H] NMR spectrum of the organic waste obtained using the HR-MAS NMR technique is shown in Figure 2a, where the carbon spectrum of Sample 0 (in blue) is compared with an OFMSW spectrum found in literature and obtained using the CP-MAS NMR technique (in black) [26]. Although the two spectra show a similar distribution of the peaks, an improvement in resolution is clearly visible in the HR-MAS spectrum in which the signal lines are much narrower. Figure 2b shows the NMR HR-MAS \({}^{13}\)C-\({}^{[1}\)H] spectrum of Sample 0 in which the different regions are indicated. The region from 12 to 40 ppm is the classic region of aliphatic carbons signals, probably due to the presence of lipids and fatty acids in the OFMSW mixture that we used. The region from 58 to 100 ppm is due to the carbon atoms signals linked to heteroatoms. Note that this region of the spectrum has the same profile as the typical CP-MAS starch spectrum, as shown in the box of Figure 2b where the comparison of this region is reported [31]. From 125 to 130 ppm, this is the region of unsaturated carbon atoms signals, i.e., signals due to unsaturation in fatty acids and/or to aromatic species; finally, the region from 169 to 183 ppm is related to the signals of carbonyl carbons (acids, esters, ketones, amides, and aldehydes). A detailed list of the overall chemical shift range of carbons is shown in Table 1 and these chemical shift ranges are used to evaluate the area of the signals. Indeed, unlike the CP-MAS spectrum in which it is possible to integrate only large signal ranges, in the spectrum of Figure 2b, the good resolution allows a better integration on the individual signals. In particular, the area of each signal of the spectrum was integrated and the quantitative information was grouped according to the nature of the atoms (aliphatic carbon atoms: \(\mathbf{C_{aliph}}\); carbon atoms linked to heteroatoms: \(\mathbf{C_{X}}\); unsaturated carbon atoms: \(\mathbf{C_{unsat}}\) and carbonyl carbon: \(\mathbf{C_{carb}}\)). In Table 2, the \({}^{13}\)C NMR integrated area of the different carbon type of Sample 0 are reported. In order to understand if the HR-MAS method is able to appreciate the possible chemical differences among the initial organic substrate and the products after the oxidative process, three samples, Sample 1, Sample 2, and Sample 3, were analyzed. The three samples are related to oxidative processes in which the initial OFMSW matrix was treated with the same amount of FeSO\({}_{4}\) but with different quantities of H\({}_{2}\)O\({}_{2}\). It is worth noting that the carbon spectra of Sample 1, Sample 2, and Sample 3 have the same spectral profile of Sample 0 and not substantial variations in the chemical shift values were observed in the spectra of the four samples (see Figure S1). The integration process on the various types of carbon was repeated for these samples and the results, reported in Table 2 and illustrated in Figure 3, were compared with the corresponding values obtained for Sample 0. Each sample analyzed shows different contents of \(\mathbf{C}\) containing groups, and these fluctuations cannot be attributed to the error in the evaluation of the integral area, but, evidently, they derive from the different oxidative processes. The greatest variations occur for the aliphatic zone and for the region concerning the carbons linked to heteroatoms.