it was improbable that many Christians were present at Pompeii, that (2) first century-Christians would have written the square in Greek and not Latin, that (3) the Christian concepts of Alpha and Omega only appear after the first century, that (4) the symbol of the cross only appears from about A.D 130–131, and that (5) cryptic Christian symbols only appeared during the persecutions of the third century. Jérôme Carcopino claimed the Pompeii squares were added at a later date by looters, however, the lack of any disturbance to the volcanic deposits at the palestra meant that this was unlikely, and the Paternoster theory as a proof of Christian origination lost much of its academic support. Regardless of its Christian origins, many academics considered the Paternoster discovery as being a random occurrence to be mathematically impossible. Several examined this mathematical probability including German historian and British historian Hugh Last, but without reaching a conclusion. A 1987 computer analysis by William Baines derived a number of "pseudo-Christian formulae" from the square but Bains concluded it proved nothing. Roman word puzzle There is considerable contemporary academic support for the theory that the square originated as a Roman-era word puzzle. Italian historian Arsenio Frugoni found it written in the margin of the Carme delle scolte modenesi beside the Roma-Amor palindrome, and Italian classist Margherita Guarducci noted it was similar to the ROMA OLIM MILO AMOR two-dimensional acrostic word puzzle that was also found at Pompeii, and at Ostia and Bolonia. Similarly, another ROTAS-form square scratched into a Roman-era wall in the basement of the Basilica di Santa Maria Maggiore, was found alongside the Roma-Amor, and the Roma-Summus-Amor, palindromes. Duncan Fishwick noted the "composition of palindromes was, in fact, a pastime of Roman landed gentry". American classical epigraphist Rebecca Benefiel, noted that by 2012, Pompeii had yielded over 13,000 separate inscriptions and that the house of Publius Paquius Proculus (where a square was found) had over 70 pieces of graffiti alone. A 1969 computer study by Charles Douglas Gunn started with a Roma-Amor square and found 2,264 better versions, of which he considered the Sator square to be the best. The square's origin as a word puzzle solved the problem of AREPO (a word that appears nowhere else in classical writing), as being a necessary component to complete the palindrome. Fishwick still considered this interpretation as unproven and clarified that the apparent discovery of the