## 3 Results and Discussion
### Characterization of the Stages during Fermentation (SF and SC) of Cocoa Beans  
A multivariate analysis was conducted through the k-means to group the fermentation times (stages) of beans in function of the antioxidant profile. The SC clusters obtained a relationship between the sum of squares between groups and the total sum of squares of 72.7%, superior to SF clusters, which was 66.8%. With these indicators, Figures 4a and 5 asuggest that the formation between groups according to the times of each fermentation is reliable. In SF (Figure 4a,b), the formation of three fermentation stages (clusters) was observed. The first group is characterized by containing the first hours of fermentation (0 h and 24 h, cluster 3) and the highest values of AA, TPC, AC, caffeine, epicatechin, and theobromine; the second group (cluster 2) was conformed by fermentation times from 48 to 72 h, which was characterized by a high content of AA (DPPH) and catechin. Finally, the next group (cluster 1) was formed by fermentation, mostly between 96 and 168 h, presenting lower values of AA, TPC, AC, methylxanthines, and flavan-3-ols. In addition to the k-means analysis, PCA showed that in SF, the sum of the first components (PC1 + PC2) explained 81.6% of the variance of the main data (Figure 4d), which was accompanied by high eigenvalues in each case (6.67 and 0.66, respectively). In the case of the first component, it can be observed that AA, TPC, AC, and flavan-3-ols are the variables with the highest correlation and contribution (4c). In contrast, in the case of methylxanthines, they make the highest contribution to the second component (higher correlation of caffeine). According to the stages formed, the first one, formed by the times from 0 to 24 h (cluster 3), is characterized by the presentation of greater astringency and bitterness [10], which, according to the data, are associated with a higher content of methylxanthines and flavan-3-ols and accompanied by a high level of TPC, AC and AA; these are similar to those determined by multivariate analysis by [PERSON] et al. [39] and [PERSON] [15; 53]. In the second fermentation stage (from 48 to 72 h), high concentrations of antioxidant profile variables were observed; these results are similar to those reported by [PERSON] et al. [4]; on the other hand, these values were lower than those observed in the first fermentation stage (cluster 3), because during this second stage, embryo death occurs, causing the leaching of cellular compounds responsible for the antioxidant profile [86]. This decrease between stages contributes to the improvement of the sensory properties of cocoa [15; 87]. In the third fermentation stage, we observed that the antioxidant profile variables studied are lower than in the first two stages, suggesting that prolonged fermentations may decrease the antioxidant potential in cocoa [15]. In SC, three stages were also obtained (Figure 5a,b), similar to those obtained by [PERSON] et al. [20]. The first stage (cluster 3, 0 to 48 h) shows the highest AA, TPC, methylxanthines, and epicatechin values. In the second stage (cluster 2), it can be observed that it shows low values of the antioxidant profile and a more significant variation in fermentation times (see Figure 5a). Finally, the third stage (cluster 1) groups mostly at times greater than 120 h, which is characterized by similar concentrations of caffeine and catechin of the first and second stages. Likewise, the PCA showed that PC1 + PC2 explained 86.0% of the variance of the data, considering the times as observations (5d), and it was noted that PC1 had a higher eigenvalue (6.96). According to the correlation circle (5c), the first component shows a more significant contribution of TPC, AA, and flavan-3 ols. At the same time, at the other extreme, we located methylxanthines and AC according to the factor map (5d), which is a behavior similar to SF. The first phase (0 to 48 h) is in agreement with previous studies reported by [PERSON] et al. [20] and [PERSON] et al.