ROME (AP) — Pope Francis has shown ‘’a truly surprising improvement’’ since returning to the Vatican to convalesce after surviving a life-threatening bout with double-pneumonia, the doctor who coordinated the pontiff’s five-week hospitalization said Saturday. “I find him very lively,’’ Dr. Sergio Alfieri said, after visiting the pope at his apartment in the Santa Marta Domus on Wednesday, three days after his release from Rome’s Gemelli hospital. “I believe that he will return if not to 100%, 90% of where he was before.’’ Francis appeared frail and weak as he greeted a crowd of well-wishers from a hospital balcony on Sunday.