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The Collaborative International Dictionary of English v.0.48:

Publicness \Pub"lic*ness\, n. 1. The quality or state of being public, or open to the view or notice of people at large; publicity; notoriety; as, the publicness of a sale. [1913 Webster] 2. The quality or state of belonging to the community; as, the publicness of property. --Boyle. [1913 Webster]