Honorius remained Pope until death and was condemned posthumously. This demonstrates that a pope can objectively fall into heresy and still remain pope and that only the Church, through an Ecuмenical Council confirmed by a Pope, can render such a judgment without compromising indefectibility.
So ... listen up, moron. "Objective" heresy, whatever you retardedly mean by the term, which never enters the debate anywhere in the entire discussion of the "5 Opinions" ... has nothing to do with losing membership in the Church. You can be "objectively" in heresy in an occult manner also. Occult "objective" heresy does not result in loss of membership in the Church (except if you adhere to one extremely minor opinion).
Despite your bloviations, which not a few people dispute, according to what's by far the most widely accepted opinion, it's MANIFEST heresy that results in loss of membership in the Church, and subsequent loss of office. If it had become manifest in 681, by that time Honorius was no longer Pope, and loss of office would have been moot, since he had long prior lost his office due to ... having died.
You need to prove that Honorius' heresy had been MANIFEST ... WHILE HE WAS STILL POPE, i.e. during his lifetime, when a loss of office could still have occurred.
He remained Pope until the end of his life because his heresy had not become manifest at any time during his lifetime. You can be sure in the early 7th century, Catholics were not shy about denouncing heresy, so it if had been evident and manifest to Catholics during his reign that he had been a heretic, the would have risen up and driven him out of the city.
You need to demonstrate that his heresy was manifest during his lifetime ... and stop being an idiot.