The Liberian Catalogue (Latin: Catalogus Liberianus) is a list of the bishops of Rome from Peter to Liberius (died 366).
The catalogue is found in copies of the Chronography of 354, a "collection of tracts .. edited (apparently by one Furius Dionysius Philocalus) in 354".
It has been suggested that it is largely dependent on a work of Bishop Hippolytus of Rome (died 235), and is his lost Chronica.
Clement’s death is recorded as having occurred sixteen years before he became bishop according to the generally received date."
The Hippolytean source is not even accurate about Pope Pius himself, who in the words of the Muratorian fragment lived "very recently in our own times".