The data for the 1035 poleis mapped in the Polis Inventory app comes directly from the website polis.stanford.edu, managed by the Stanford University Classics Department.
After the Inventory was published, other scholars, notably Josiah Ober and his colleagues and students, began to develop digital versions of the printed material in spreadsheets. The result of this effort is presented on their website and their data is made freely available to the public for academic uses and general interest and study.
Further detail about the data and more detailed accreditations than found on this website or in the Polis Inventory app itself, may be found on this Stanford website.
Keeping with this spirit of data accessibility, users of the Polis Inventory app may access a copy of the data from the "About" page in a GeoJSON format.