DICOM already provides a unique enough identifier for the Series (e.g. Series Instance UID), so why also include one on the lower level objects (e.g. SOPInstanceUID)?
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This question was from quite a while ago, but I thought I'd add that, ignoring QR altogether, a SeriesInstanceUID is a globally unique identifier for a single series. SOPInstanceUID is a globally unique identifier for a DICOM file. A series can have multiple DICOM files, so each would share that same SeriesInstanceUID, but each file would have it's own SOPInstanceUID.