"Pope/bishop Pius 1" is a fake, he really matches emperor Antoninus Pius.
-- Pius name Pius. (& was "during the [reign] of Antoninus Pius".) "like the similar error "Anicetus, Pius" for "Pius Anicetus"" -- Antoninus Pius name Antoninus Pius.
-- Pius: Born "81 ad". Reigned 140/142/146-154/155/157/161. Died/feast 11 July. (Born "11 January".) Died age "74". (& he was "during the [reign] of Antoninus Pius".) -- Antoninus Pius: Born 86 ad? Reigned 138-148-156-161. (Marcus took some role from 156.) Accession 10/11 July. Died age "74". -- Both: Both are 140-155. Both are 11 July. Both died age 74.
-- Pius: Built 1/2 churches & baptistry. -- Antoninus Pius. Authorised the construction of a temple to Faustina. "Antoninus built temples, theaters, and mausoleums...." ["newly built temple to Hadrian"?]
-- Pius: Was "Pope/Papa / Bishop / [Pontifex Maximus]" "the account of his [Justin's] martyrdom indicates there was no Roman bishop present there." -- Antoninus Pius: Was "Pontiffex Maximus" (& the "Princeps"/"Principate"?) "Antoninus was known as an avid observer of rites of religion...." "Instead of stirring up persecution against the Christians, he extended to them the strong hand of his protection throughout the empire."
-- Pius: Opposed the Valentinians. Valentinus and Marcion visited Rome during that period. -- Antoninus Pius: Chief lawyer L. Fulvius Aburnius Valens. Marcus (Aurelius).
-- Pius: "The writer of the later text identifies himself as a former slave. This has led to speculation that both Hermas and Pius were freedmen." -- Antoninus Pius: "Antoninus passed measures to facilitate the enfranchisement of slaves. Mostly, he favoured the principle of favor libertatis, giving the putative freedman the benefit of the doubt when the claim to freedom was not clearcut."
-- Pius the "9th succesor of St Peter". -- Antoninus: "900th anniversary of Rome" during his reign.
-- Pius & Antoninus: In their pictures they look similar to me?
And possibly/not these ones?:
-- Pius: "The "Liber Pontificalis" speaks of a decision of this pope to the effect that Jewish converts to Christianity should be admitted and baptized. What this means we do not know...." -- Antoninus Pius: "Scholars place Antoninus Pius as the leading candidate for fulfilling the role as a friend of Rabbi Judah the Prince"?
-- Pius: "Martyr (by sword)". But they otherwise say it was a conjecture and is no grounds for consideration, and is not presented as martyr in 'Roman Martyrdom'. -- Antoninus Pius: Peaceful non-miitary reign, which some say is his fault/blame in causing troubles later after him. Incinerated on pyre at Campus Martius. [Martyrdom of St Justin?]
-- Pius: Uncertainty whether Pope/Bishop in 155/156 was Anicetus/Anicitus or Pius or none? -- Antoninus Pius: The name Anicetus could be linked with either A(ur)elius Antoninus (Pius), or (Marcus) Aurelius Antoninus, or (Marcus/Lucius) Aurelius Verus? Or the meaning of Anicetus "unconquered" may relate? Or his attribute of palm branch with peaceful reign of Antoninus?
Not sure of the correct match for this one, but:
-- Pius: "Born at Aquileia, Friuli". ["of Illyrian origin".] -- Antoninus Pius: "... the free access of the people of Rome to drinking water was expanded with the construction of aqueducts...." [Though Aquileia may be aquilo eagle, or god Aquilo, not aqua water.] The Aurelii? Password Aequanimitas? [Born at Lanuvium. From Nimes. Ancestral estate Lorium, Etruria.]