## 2 Materials and Methods  
### Study Design  
The present study was conducted in accordance with the Declaration of Helsinki and the Professional Code of Conduct for Physicians of the Bavarian Medical Association in their current versions. As part of this study, all consecutive patients who underwent tooth extractions in the posterior region of their upper jaw at the University Hospital Wurzburg between 2010 and 2022 were included. The following criteria were excluded from consideration: malignant diseases around the surgical site, fractures at the surgical site, syndromal anatomical variants, inflammations on the root tip, and chronic/pre-existing OACs. In addition, only images of comparable quality were included. Careful attention was paid to obtaining good positioning of the facial planes and symmetrical alignment of the head while avoiding projection-related enlargements or reductions. Only one type of X-ray machine was used during this period. Externally scanned images were also excluded due to the lack of comparability. A total of 357 patients with extracted teeth and the associated imaging were consecutively included. This study was approved by the Ethics Committee of the University of Wurzburg before the start of the study and was authorized under authentication number 2022011702.  
Following approval by the ethics committee, data were extracted from the data management system of the University Hospital of Wurzburg. The screening was conducted on patients who had tooth extractions in the maxillary posterior region between 2010 and 2022. Patient identification was based on ICD codes. A detailed review of the operation reports for the group of patients who had an OAC following tooth extraction was conducted. The preoperative panoramic radiography was extracted if OAC could be determined clinically through various examinations. Images were anonymized before being processed. As for the control group, all patients who had a posterior extraction were screened and allocated to the control group after reviewing the surgical report in which OAC was not diagnosed or excluded. We extracted the radiographs in the same manner as described above. The included patients had 2 nd and 3 rd molars in undisturbed occlusion with regard to their dentition. This was necessary in order to be able to give a reliable assignment to the classifications used, Archer and RS. Since the extraction of 3 molars is one of the most common procedures in dentistry and oral and maxillofacial surgery, we have a homogeneous distribution with regard to gender. One study has already shown that there is no significant difference in the probability of OAC occurrence in relation to gender [4]. Furthermore, with a median age of 28 years, this procedure is mainly found in young patients. We were able to confirm this age distribution in our study. As we anonymized the images directly after extraction and focused on the exclusive detection of the probability of postoperative OAC using the classifications, no subgroup analysis of the data was performed. In total, 157 cases were collected in the OAC group and 200 consecutive cases in the control group for analysis. Thereafter, the region of interest for the classification system (upper quadrants) was selected, and images that were not suitable for classification (e.g., lacking the third molar) were excluded. Two experts in oral and maxillofacial surgery subsequently set the ground truth of the RS and Archer clinical classification systems. Disagreements regarding the classifications were resolved by discussion with a third reviewer. The regions of interest were identified and cropped from original panoramic radiographs. The definition of the ROI was performed manually by two annotators in this work. Care was taken to standardize the ROI-defining process and to not allow too much variability due to potential artefacts (e.g., metal artefacts). The final number of classes was as follows: Archer A (n = 126); RS I, II, V (n = 130); Archer B-D (n = 365); RS III, IV (n = 361).