What "singularity"
The kind that changes with the passage of time?
Like priests can be married/can't be married/whatever.
Or like the differences that exist between the Roman church and the EO, both of which think they are the original, true to form church and the other branch is in schism?
Sigh....another day that you missed in Catechism class...unmarried priesthood is a simple rule which could be changed at any time....has no bearing on Catholic dogma whatsoever. The schism was exactly that....the Roman church existed and there were those who wished to challenge the papal authority.....now, the Pope had been in existence for a long long time before the schism, therefore it was the eastern church which split.....All, however, are still true and faithful Catholics and will someday, probably soon, reunite their groups.