So let me see if I got this right:
At some point, due to strictly disciplinistic (is that a word?) and/or stylistic disagreements, there was a split in the early church, into partition A and partition B.
At this point, the split was minor and did not actually separate the church from being in communion with each other?
In the early church there were regional differences (custom mostly) in how worship was to be performed. All the basics were in place but there were regional variations. Not a problem.
There were also differences in spirituality, this being mainly due to the uneven distribution of manuscripts, I think. The liturgical prayers also varied, and the way people thought about God was influenced by their prayer life. Some writers were better known in one region than another. Not a problem.
The church decided early on to organize the regions (as synods) around certain Metropolitan bishops: Egypt (and nearby lands) was under the Metropolitan at Alexandria, Italy (and nearby lands) was under the Metropolitan at Rome and Syria/Asia was under the Metropolitan at Antioch. We have come to call these most esteemed bishops patriarchs. Not a problem.
Later Constantinople and Jerusalem were added to this list to make five Patriarchates, or the Pentarchy. Rome was seen to be the most esteemed, especially due to it’s origins in the work of Ss Peter and Paul. Not a problem.
Much of the issue today is over the patriarchate at Rome. There is no agreement on how much actual authority the bishop of Rome (called the Pope) has had in the past, or should have going forward.
Since the schism of 1054AD, bishops of Rome have called Councils in the west and defined new dogmas. These did not apply in the east. The Popes would like the eastern churches to accept these new Latin dogmas, the Patriarchs in the east would like the Popes to withdraw the new dogmas.
So far, no real progress either way.
We all want to get along, and have much in common.
Then later, one of the partitions, say A, defined a dogma that said the Pope is infallible when speaking ex cathedra on matters of faith and morals.
That is correct.
This was in 1870AD, about 820 years after the schism.
Since the partitions had already split by this point, partition B is not required to adopt this new dogma in order to still be considered in communion with partition A.
Not quite right.
The two ‘partitions’ are not in formal communion. Partition A has recognized the validity of partition B, but B is not entirely sure of A anymore and does not comment upon the validity of A. It’s up in the air.
The two church groups do not concelebrate. In other words when hierarchs (now on more friendly terms) are visiting they do not jointly share in confecting the Holy Eucharist or other sacraments. Communion is definitely impaired.
Some day that might change.
So because of this, partition A and partition B disagree no longer on simply disciplinary issues, but now instead disagree on a dogmatic issue and are still in communion with each other.
No. They are not in formal communion. Partition A has stated or implied that partition B, while true churches, are defective for not having the Pope as their spiritual leader and practical administrator. Partition B for their part tend to think partition A are defective as well, which is evidenced by the refutation of errors most converts from A are expected to make.
BUT, let’s start over, and say it happened like this:
The early church splits into two partitions, A and B. A and B disagree on some dogmatic issue that was defined before the split, then they are not in communion with each other?
No, that does not apply here.
