**Appendix A**

The differences in δ<sup>C</sup> (CD3OD, Figure 5a,b and Figure A1a,b) of allylic –Н**C**(OOH)– (Δδ<sup>C</sup> = δ<sup>C</sup> *trans* − δ<sup>C</sup> *cis* = 88.2 − 82.5 = 5.7) and –Н**C**(OH)– (Δδ<sup>C</sup> = δ<sup>C</sup> *trans* − δ<sup>C</sup> *cis* = 74.4 − 68.7 = 5.7) were close to the corresponding values (CDCl3) of *trans*-monoenoic and *cis*-monoenoic allylic hydroperoxides (Δδ<sup>C</sup> = 86.9 − 81.1 = 5.8) and allylic alcohols (Δδ<sup>C</sup> = 73.1 − 67.5 = 5.6), calculated in accordance with data in the literature [43]. Additionally, the signals of –НC(OH)– of *trans*-monoenoic allylic alcohols (δН 3.94, Figure 5b) were shifted upfield (by 0.42 ppm) compared to their *cis*-isomers (δН 4.36, Figure A1b), as described for *cis*/*trans*-isomeric methyl 12-hydroxyoctadec-10-enoate and 9-hydroxyoctadec-10-enoate in CDCl3 ([44]: Δδ<sup>H</sup> = δ<sup>H</sup> *cis* − δ<sup>H</sup> *trans* = 4.4 − 4.0 = 0.4). Similarly, the signals of –НC(OOH)– of *trans*-monoenoic hydroperoxides (δН 4.16, Figure 5a) were shifted upfield (by 0.46 ppm) compared to their *cis*-isomers (δ<sup>Н</sup> 4.62, Figure A1a), as observed earlier ([45]: Δδ<sup>H</sup> = δ<sup>H</sup> *cis* − δ<sup>H</sup> *trans* = 4.68 − 4.22 = 0.46 for *cis*/*trans*-isomeric hydroperoxides of methyl oleate in CDCl3).

**Figure A1.** Some δ<sup>H</sup> (500 MHz) and δ<sup>C</sup> (125 MHz) values for trace *cis*-monoenes with allylic (**a**) hydroperoxy or (**b**) hydroxy groups (solvent: CD3OD).

#### **Appendix B**

Although a single peak in the GC chromatogram represented overlapping esters of four isomeric keto acids, the mass spectra, obtained from different points in the GC peak, exhibited fragmentations of samples, enriched in the isomers with keto groups in the (*n*–9)→(*n*–8)→(*n*–7)→(*n*–6) positions (in this order of elution). Mass spectra of methyl esters of minor keto C23 and C22 acids displayed homologous pairs of *m*/*z* 141/156 and 99/114 fragments, containing methyl ends of the molecules with keto groups on the (*n*–9) or (*n*–6) carbon, respectively (Figures S12, S13, S15, and S16). The total mass spectra, obtained by averaging the spectra over the selected GC peaks, showed significant differences between relative abundances of several ions, characteristic of different isomers. For the overlapping esters of 15-keto, 16-keto, 17-keto, and 18-keto C23 acids, the abundance ratio of the characteristic ions of *m*/*z* 342, 356, 370, and 384 were about 1:3:3:1 (Figure S14). Accordingly, the mixture of C23 acid derivatives contained significant amounts of isomers with a keto group in the (*n*–8) and (*n*–7) positions and minor amounts of isomers with a keto group located at the (*n*–9) and (*n*–6) positions. The overlapping methyl esters of homologous keto C22 acids exhibited similar fragmentation and elution behavior.

GC-MS analysis also revealed the presence of clusters of closely overlapping chromatographic peaks for derivatives of regio-isomeric diacetyloxy C23 and C22 acids, including minor components. In particular, the α-fragments included the ions of *m*/*z* 371 and 413 (Figures S17 and S18) for the derivatives of 2,15-diacetyloxy and 2,18-diacetyloxy C23 acids, respectively, and the ions of *m*/*z* 357 and 399 (Figures S19 and S20) for the 2,14-diacetyloxy and 2,17-diacetyloxy C22 acid derivatives, respectively. The abundant ions of *m*/*z* 269 and 311 (Figures S17 and S18), which were detected in the mass spectra of the methyl esters of isomeric minor 2-acetyloxy C23 acids, confirmed the presence of second acetyloxy groups on C-15 and C-18, respectively. Similarly, *m*/*z* 255 and 297 ions in the mass spectra of the methyl esters of minor 2-acetyloxy C22 acids (Figures S19 and S20) indicated a second acetoxy group on C-14 and C-17, respectively. α-Fragmentation of isomers with an acetyloxy group in the (*n*–9), (*n*–8), (*n*–7), or (*n*–6) positions (in this order of elution) and subsequent loss of AcOH gave rise to *m*/*z* 125, 111, 97, and 83 ions, respectively, containing the methyl end of acyl chains. Among these α-fragments, the largest fragment of *m*/*z* 125 was much less abundant than the related ions. Unfortunately, the percentages of all the methyl esters of isomeric diacetylated FAs, which were only partially separated by GC, could not be accurately evaluated on the basis of mass spectral data because the presence of diagnostic α-fragments, formed from isomers with an acetyloxy group in the (*n*–9) positions, were masked by other peaks in averaged mass spectrum. However, for diacetyloxy C23 acid derivatives with an isolated acetyloxy group in the (*n*–8), (*n*–7), or (*n*–6) positions, the abundance ratio of the diagnostic α-fragments of *m*/*z* 385, 399, and 413, respectively, were about 3:3:1. The abundance ratio of homologous α-fragments (*m*/z 371, 385, and 399) were nearly the same for the derivatives of diacetyloxy C22 acids. Accordingly, the spectra, recorded at the top of the most intense overlapping GC peaks, exhibited fragmentation patterns of major isomers with an acetyloxy group in the (*n*–8) or (*n*–7) positions, while the mass spectra, recorded at lower points, belonged to minor isomers with an acetyloxy group on the (*n*–9) or (*n*–6) carbons.

We assumed that the abundance ratio of components with oxygen-containing groups on the (*n*–9), (*n*–8), (*n*–7), or (*n*–6) carbons (about 1:3:3:1, respectively) were nearly the same for isomeric hydrogenated products and initial hydroperoxy FA moieties. This suggestion was supported by (–)ESI-MS/MS study of isomeric allylic hydroperoxides (Figure 4a), showing two pairs of characteristic peaks with a 3:1 intensity ratio, including peaks at *m*/*z* 743.6/729.55 (fragments, formed from acyl chains with –OOH in the (*n*–8)/(*n*–9) positions) and *m*/*z* 784.6/798.6 (fragments, formed from acyl chains with –OOH in the (*n*–7)/(*n*–6) positions). Thus, the previously mentioned minor hydrogenated products were possibly derived from minor amide-linked FA with allylic hydroperoxy/hydroxy/keto groups in the (*n*–9) or (*n*–6) positions. However, complete structures of the corresponding oxidized cerebrosides could not be comprehensively elucidated due to their minor amounts. Therefore, only major cerebrosides with oxygen-containing groups in the (*n*–8) or (*n*–7) positions of acyl chains were the focus of our research.
