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The Collaborative International Dictionary
Pseudonymousness

Pseudonymous \Pseu*don"y*mous\, a. [Gr. ?; pseydh`s false + ?, ?, a name: cf. F. pseudonyme. See Pseudo-, and Name.] Bearing a false or fictitious name; as, a pseudonymous work. -- Pseu*don"y*mous*ly, adv. -- Pseu*don"y*mous*ness, n.

Wiktionary
pseudonymousness

n. The quality of being pseudonymous.