Reconstructing ancient papyri from fragmented pieces is a demanding task, posing significant challenges for papyrologists due to degraded material, subtle texture cues, and a lack of distinct landmarks. This paper introduces JoinPap, an intelligent interactive system designed to foster human-machine collaboration in this specialized domain. JoinPap leverages a self-supervised convolutional autoencoder, trained with a contrastive learning objective on high-resolution papyri scans, to acquire robust and discriminative texture-aware embeddings. These representations capture the continuity of fiber patterns across fragments, enabling a specialized matching algorithm to propose optimal vertical and horizontal alignments. We elaborate on data preparation, network design, training methodology, and integration of the matcher into a user-centered interface that supports fragment manipulation and annotation. JoinPap effectively supports expert-in-the-loop reconstruction by offering high-quality alignment suggestions grounded in visual texture continuity.