Attempting to contribute and nominate a web map that includes a basemap in a custom projection to Living Atlas of the World shows the message "Error: Provide a geometry service to open Web Map." and the web map is unable to load as expected.
Last Published: April 17, 2017ArcGIS Online
Bug ID Number
October 26, 2015
August 21, 2020
Operating System Version
7.0 64 Bit
After review by the development team, it has been determined that this issue is related to a known limitation with the software that lies outside of Esri's control. The issue's Additional Information section may contain further explanation.
That's a known limitation for now. Right now its not in the current roadmap.
Use a basemap with a spatial reference of Web Mercator (auxiliary sphere) (102100) with non-tiled layers in the custom projection. The tiled basemap layer can be used if it is recreated in the Web Mercator Auxiliary Sphere Projection.