You are aware the that the first attested use of the word Catholic is from the successor of St. Peter (and ordained by him) St. Ignatius? But that was at St. Peter’s first See, Antioch, and he was wrtiting to another Church in the East (Smyrna). He did write a letter to Rome, but it doesn’t mention the bishop let alone pontiff there

Oh, btw he was martyred, like MANY MANY of the Patriarchs of the East.
****Forgive me but you have St. Ignatius in the time of St. Peter the first Pope? Ignatius of Antioch lived in the time of St. John and St. Polycarp. I question your sources here? ST. Ignatius was loyal to the Chair of Peter, as was St. John.
Yes most of the great Eastern Saints and Martyrs all acknowledged the Pope. Arianism came from the East. St. Cyril was undersuspicion from the Pope, because he was baptised by an Arian Priest. You cant change history no matter your opinion. I dont think I need to list all the eastern fathers who went into apostacy by publicly or in writing succumbed to the death threats from the Pagan Roman Emperor, and they made sacrificed to Idols, and were excommunicated by the Pope, while the western bishops and popes were being martyred for refusing to apostacize, or allow heretical teachings into the Church.
St. Ambrose an eastern saint, wanted to re-baptise these eastern bishop apostates back into the Catholic church after they repented. But the Pope told St. Ambrose NO, you can only be baptised once. Needless to say, St. Ambrose did not like the Pope’s decision but obeyed the authority of Peter’s chair from the Pope. The Pope accepted their repentance and admittance back into the Church. Just as Peter returned his disciples back into the fold of Jesus, Just as described in Scripture.
Truthfully I dont know what you are trying to accomplish here, other than offer your heretical opinions about the Magesterium and decisions that you appear to have conflict with. What you are implying as heretical by the Popes who excommunicated or denied your change to apostolic teaching and authority. Thus far you have only entered your opinion about a historical topic without no factual evidence to support it. What matters when you look to these councils is the outcome and measure it against the Oral apostolic Traditional teachings and Sacred Scripture, before you enter your negative opinion or view. Instead of complaining, just state your disbelief, excommunicate yourself, or fall into full communion with Peter’s Chair the present day Pope, or remain in schism.B]****
Oh, the West at least since the Reformation has been quite the hotbed of heresy, And not only have you managed to recycle our heresies (btw, Aranism lived on in the West) but far outdone them (we don’t have anything to match the Mormons).
**I have heard this view before that the Roman Church is responsible for the Reformation. While I cannot disagree with you on the protestant heresies, such as Mormonism etc. The Roman Catholic church has already spoken about the reformation activities and remains unchanged about these seperating sects that continue to divide. But note this, The Authority of Peter in the Pope and the successors of the apostles are alive and still active resisting heresies that come against her. Jesus already promised us the good news, the gates of the netherworld will not prevail. Although the west in the America not Rome is plaqued with heretical christian teachings, these heretics although are quite knowledgable, do not subscribe to the Catholic church, if anything they protest the authority of the Catholic church and her apostolic teachings.
Peace**