In study we attempt to solve the problem of determining how authentic published images on the Internet are, and to what degree they may be identified by comparison to the original image. The technique proposed aims to serve the new requirements of libraries. One of these is the development of computational tools for the control and preservation of intellectual property such as digital objects, and especially of digital images. For this purpose, this article proposes the use of a serial number extracted using a previously tested semantic-properties method. This method, based on the multilayers of a set of arithmetic points, assures the following two properties: the uniqueness of the final extracted number, and the semantic dependence of this number on the image used as the method's input. The major advantage of this method is that it can serve as the authentication for a published image or detect partial modifications to a reliable degree. Also, it requires the better of the known hash functions that the digital-signature schemes use, and produces alphanumeric strings for checking authenticity and the degree of similarity between an unknown image and an original image. As an example of a possible application, this article suggests that this method could be incorporated into the well-known DOI system in order to provide a reliable tool for identification and comparison of digital images.