There is one image of the front side of the pottery piece you have (the others attached are of a book cover).
There is a Japanese writing on the one side. Are there any marks on the underside of this?
What are some of the theories that you have heard on this piece?
Thank you for the additional information and info. That is certainly a range of information given to you and if this is 14th century, it would take more in-depth research and study on it than can be provided online. Have you attempted to contact any Asian specialty departments at auction houses such as Christies, Sotheby's or Bonham's?
Understood. I do suggest I.M. Chait for help on this. My opinion is that that incised white areas are 'too clean' for 14th century. I will opt-out and open your question here to all the experts again for you. I do hope you find the information that you seek. Sincerely, Nora