"Paul claimed was alive a certain Jesus who had died"

Festus referred Paul's case to the king, saying,
"There is a man here left in custody by Felix.

His accusers stood around him,
but did not charge him with any of the crimes I suspected.
Instead they had some issues with him about their own religion
and about a certain Jesus who had died
but who Paul claimed was alive."

-- Acts 25:13b-21

The first Christian communities lived this form of fellowship intensely. Thus the Apostle Paul gives them a share in his ministry of preaching the Gospel but also intercedes for them. The intercession of Christians recognizes no boundaries: "for all men, for kings and all who are in high positions," for persecutors, for the salvation of those who reject the Gospel.

-- CCC 2636

The mystery of Christ's resurrection is a real event, with manifestations that were historically verified, as the New Testament bears witness. In about A.D. 56 St. Paul could already write to the Corinthians: "I delivered to you as of first importance what I also received, that Christ died for our sins in accordance with the scriptures, and that he was buried, that he was raised on the third day in accordance with the scriptures, and that he appeared to Cephas, then to the Twelve. . ." The Apostle speaks here of the living tradition of the Resurrection which he had learned after his conversion at the gates of Damascus.

-- CCC 639