## 3 Results and Discussion  
### In-House Validation of the Analytical Outcome  
Although there is not a consensus yet on the procedure to validate fingerprinting analytical methods, and precise guidelines have not been established, ensuring the quality and reproducibility of analytical results is a necessary condition to posit a method as an authentication screening tool. As fingerprinting methods are not aimed to the identification and quantification of analytes but to find distinctive patterns specific for a given food category (i.e., virgin olive oil commercial category) in raw analytical signals (i.e., chromatograms), the main constraint is providing a repeatable and reproducible signal with enough sensitivity to collect valuable information from the samples. For this purpose, we proposed some performance criteria to evaluate the repeatability of the analytical outcome, provided that the system suitability fulfilled the minimum requirements.  
On the one hand, as suggested by [PERSON] et al. (2019), we evaluated the RSD of each data point in the chromatogram that had an intensity above mean noise. After noise subtraction, the number of variables decreased to around 70% of the initial signals. The FDA indicates that RSD values of 15% are generally acceptable as regards analytical variability for target analysis, except for concentrations close to the detection limit where an RSD of 20% is acceptable ([PERSON] et al., 2019). Even though in this work we chose a fingerprinting approach, where more variation is expected, the previous reference was used as a benchmark towards the repeatability assessment. Here, 99.3% and 98.0% of the variables presented RSD equal or below 15% when assessing intra-day (Supplementary Material, Figure S1a) and inter-day (Supplementary Material, Figure S1b) repeatability, respectively, which was in accordance with the FDA recommendation. The RSD was also used to assess chromatographic fingerprints obtained by FGC, achieving comparable outcomes ([PERSON] et al., 2019). When the RSD was plotted versus the signal intensity for intra-day (Supplementary Material, Figure S1a) and inter-day repeatability (Supplementary Material, Figure S1b), both plots showed that the higher the signal intensity, the lower the RSD. This agreed with the trend described by the [PERSON]'s equation, formulated for targeted methods, and proved that the repeatability was strongly correlated with the intensity of the variables ([PERSON] et al., 2019).  
On the other hand, the precision of the analytical signal was also evaluated by the clustering of QC samples in a PCA (four principal components, 73.3% of explained variance), as proposed by [PERSON] et al. (2019) for untargeted metabolomics, which supported the above-mentioned findings. Here, tight clusters at the centre of the score scatter plot were observed for the QC samples analysed for intra-day and inter-day repeatability, which according to [PERSON] et al. (2019), indicated a precise analytical outcome (Figure 2a). These QC clusters were located close to EVOO and LFH control samples, pointing out the strong weight of the variables related to these sensory profiles (Figure 2a). Furthermore, the residual standard deviation plot of the PCA showed that both intra-day and inter-day replicates were under the critical value (0.05), confirming no deviations in their distance to the PCA model (Figure 2b).