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I have created a node with a required field.
Anonymous users have permission to create nodes of this type, but do not have permission to edit the required field on creation.
When anonymous users save the node they are taken back to the node creation form with no values filled in the title / body fields and no error message.
1. It would be nice for their to at least be an error message (bug)
2. It would be nice if the former values in the other fields were filled in (bug - loss of data)
3. It would be nice if required setting was available on a per role basis, or if the field was not required for those without edit access to it. (feature request, but not sure if field API would allow this)