I would like to know if Mobile Push filtered lists can be created programmatically. I couldn't find any details other than refreshing a list in the support documentation.
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If you look at the API calls that SFMC is doing when creating the list in MobilePush in Mobile Studio, you will see that it is sending to an internal endpoint (not able to be accessed by outside resources) to create the lists. This combined with the fact that there is no interaction in Automation Studio for creation of lists - only refresh, means that neither the UI nor the API provide you the ability to automate this process.
Interestingly enough, if you notice that the internal API is related to Audience Builder and not Contacts or Push. It doesn't really add much here, but just thought it was interesting and worth pointing out.