### Experimental Conditions and Sample Preparation  
\({}^{13}\)C SSNMR experiments on OM samples in waste management are generally carried out on spectrometers working at \({}^{13}\)C Larmor frequencies of 75-125 MHz, although a frequency of 150 MHz is used in more recent studies and frequencies as low as 25 MHz were employed in the oldest ones. MAS rotors with diameters of 4 mm, containing a few tens of milligrams of sample, and MAS frequencies of 8-13 kHz were usually employed. Few cases are also reported where rotors with 7 mm diameter and spinning rates of 3.5-5 kHz were used. As said, \({}^{13}\)C CP-MAS experiments are usually performed with a contact time of 1 ms, although cases are reported where longer contact times (2-3 ms) were used. In these experiments, the recycle delay ranges from 0.5 to 5 s and a few thousand scans are acquired.  
Before \({}^{13}\)C SSNMR experiments, OM samples are simply dried (by freeze-drying, oven-drying at 40-110 \({}^{\circ}\)C, or air-drying), ground, and possibly sieved to obtain a fine powder; the latter operation is not strictly necessary, but it is useful since it ensures stable sample spinning and, consequently, a good spectral resolution. Considering that only a few tens of milligrams of powder are necessary for the analysis, accurate sampling and homogenization are critical to obtain a representative sample.  
Several studies on compost and vermicompost, focused on extracts, instead of investigating the bulk material. Different types of extracts were investigated, that is, humic substances (HSs), dissolved organic matter (DOM), or compost tea (CT). Humic substances are stable compounds with a complex and variable composition, mainly containing aromatic rings linked by methylenic chains and/or oxygen atoms, with carboxyl and hydroxyl groups bonded to the rings and the alkyl chains. On the basis of their solubility, two different extractable HS fractions can be obtained, i.e., fulvic acids (FAs, soluble at any pH value) and humic acids (HAs, soluble at pH > 2). The extraction of HSs is performed by mixing the dry compost in an alkaline solution; HAs can then be separated by acidifying to pH 1.0. HAs have higher molecular weight and degree of aromatization with respect to FAs, which, on the other hand, are richer in carboxyl and hydroxyl groups [54]. Thanks to their highly aromatic structure, HAs are stable compounds and their amount is typically considered as a measure of compost maturity [55]. In fact, during composting HAs tend to increase whereas FAs tend to decrease [56]. Compost DOM is a mixture of low-molecular weight compounds, such as sugars and free amino acids, and high-molecular weight compounds, among which are also HSs [57]. DOM is a very small fraction of the total organic matter present in compost, decreasing as feedstock stabilization proceeds, but it is an important component since many biochemical transformations that occur during composting take place in solution. DOM is extracted from compost by shaking the material with ultrapure water; DOM can be further divided into a hydrophobic fraction (HoDOM) and a hydrophilic fraction (HiDOM) using Amberlite(r) XAD-8 or Supelite(tm) DAX-8 resin [57]. Finally, compost tea is an aqueous extract obtained from the fermentation of compost in water either in forced aerated or non-aerated conditions [58].