Did Matthias or Paul replace Judas Iscariot as the twelfth apostle?

Matthias replaced Judas and became a member of the closed apostolic group of twelve. To be a member of this group, one had to have been with the Messiah from the time He was baptized by John until His ascension. The second category of apostleship had a more limited prerequisite, which was seeing the resurrected Messiah. Both Matthias and Paul qualified for the second category, but Paul did not qualify for the first category. The book of Acts nowhere indicates that the choice of the apostles was wrong. When the Spirit came upon the apostles in Acts 2:1-4, it included Matthias but would not have included Paul since he was not yet saved.