Dates match: Pope Clement 1 (68-76 or) 88/91/92-92/97/99/100/101 (compiled from sixe different official popes lists). Emperor Domitian reigned 81-96/97. (Domitian aided in the admin of the empire in 69(-?). Received title of Caesar in 69 or 71? Ceremonial heir 71-81.) Both dates coincide (69/71-76 &) 88-96/97; end date 96/97 matches; similar start dates 81/91.
Both associated with the name Clemens: The 4th pope's name is Clemens/Clement. Emperor Domitian's cousin is Titus Flavius Clemens (and both Domitian & Clemens had the same first two names). Another family member was (Marcus) Arrecinus Clemens. Both names/persons are associated with each other in the quote "for kata ton deloumenon is meaningless if it is taken to refer to Clement and not to Domitian".
The meaning of the name Clement "clemency" seems an inversion of the 1st/2nd persectution of Christians under Domitian. Domitian's persecution policy/declaration, "no christian exempt from punishment". "Domitians tyranny".
Number match: Clement is 4th from pope "Peter" (who matches Nero). Domitian is 4th from Nero (who matches pope "Peter") excluding the 3 "usurpers" of 69 ad. (Domitian's great-grandfather's surname was Petro.)
In some popes lists Clement is second pope after Peter (who matches Nero). Domitian was considered a reincarnation of Nero (who matches pope "Peter"). (Plus, 1st persecution under Nero, 2nd persecution under Domitian.)
Both connected with the senate: Clement was a "member of the Roman senate". Domitian "received the education of a young man of the privileged senatorial class...." "Domitian acted as the representative of the Flavian family in the Roman Senate." "these offices no doubt gained Domitian valuable experience in the Roman Senate....".
Clement: 'Clemens Romanus' "Clement of Rome" ("born in/at Rome"). Domitian: born in/at Rome.
Clement: The Clement of the bible was "probably a Philippian". Phil-ip means "lover of horses". Domitian: "qualities he found more often in men of the equestrian order...." "relying on a small set of friends and equestrians...."
Clement "probably knew Timothy". Domitian considered contemporary of Timothy.
Clement: Clement issued '1 Clement', the basis of apostolic authority for clergy. Domitian: "Domitians tyranny". Domitian's persecution policy/declaration, "no christian exempt from punishment". "nominating himself perpetual censor, he sought to control public and private morals. As a consequence, Domitian was popular with the people and army...." "... allege that Domitian officially gave himself the title of Dominus et Deus."
Both were pontiffex maximus. Clement is bishop / "pope" / "pontiffex maximus" / "supreme pontiff" (Annuario Pontificio, Liber Pontificalis). [Ignatius letter to Rome doesn't mention a bishop.] Domitian was pontiffex maximus (the emperors from Augustus to Gratian were pontiffex maximus). "the Senate confirmed Domitian's powers, granting tribunician power, the office of Pontifex Maximus, and the titles of Augustus, and Pater Patriae." Domitian statue in Vatican Museums. [The argument that the titles pontiffex maximus and pope were not used by/for bishops of Rome until later (mid-5th & mid-6th centuries) and so is an anachronism is not necessarily valid because bishop/pope/pontiff are still related/similar.]
With both the popes & emperors before & after also match all in order. 1 Peter (Nero) = Nero (Peter) 2 Linus = Vespasian 3 Cletus = Titus 4 Clement 1 = Domitian (Clemens) 5 Evaristus = Nerva 6 Alexander 1 = Trajan (Alexander) 7 Sixtus 1 = Trajan? or Hadrian? 8 Telesphorus = Hadrian? 9 Hyginus (Graecvs) = Hadrianus (Graeculus) 10 Pius 1 = Antoninus Pius etc. See each separate pope & emperor chapter for matches details.
Clement: "Martyred". Domitian: "T. Flavius Clemens... was martyred by his first cousin, the Emperor Domitian". Domitian assassinated by court officials. Domitian persecution of Christians the 2nd of 10 persections from Nero to Diocletian. (Inversion.)
Clement: "papal Tiara" [grand Crown]. ["absolute & universal authority"?] Catholic source suggests Clement may have been a freedman of the emperors household. Domitian: Was emperor.
Clement: Stone quarry; stone cutters. "the House of Clement. Domitian: "initiated a massive building program". Erected vast Flavian Palace / House of the People on the Palatine Hill. Finished the Temple of Vespasian & Titus. Arch of Titus completed in reign of Domitian.
Clement: Contradiction of sources on whether he was ordained by Peter, and contemporary of Peter & Paul, and "saw the apostles ...", or was 24 yrs later or 36 yrs after the apostles. Domitian: Domitian considered a reincarnation of Nero under who Peter & Paul supposed to have been martyred. The persecution mentioned/implied in epistle of Peter is thought by some scholars to be the Domitian one.
There is no contemporary proof of existence of any pope Clement 1. Their sources use words like "Probably", "most likely", "according to ... claimed", "most of the Latins held", "opinion". Though Clement is "widely mentioned by Christian writers in the second and third centuries" including by Dionysius, Irenaeus (ca 180/195), Tertullian (ca 199), Eusebius ca 325, Jerome (ca 393/396), and Isodore (9th cent), and Clement's epistle to the Corinthians "was considered to be a canonical New Testament book by a great many authorities in the early church" and it was known to Athanasius and it was included in the 5th century codex Sinaiticus. But this may just mean that they first started the emperors/popes correspondence as early as Irenaeus. Historians say the letter 1 Clement is spurious. There is no certainty that pope Clement is the same as the Clement mentioned in Philippians in the bible.