New Sun Religion #10
Extracting material from Gene Wolfe’s The Book of the New Sun: A Chapter Guide (2019), putting it into dictionary form, the following:
Theologoumenon (II, chap. 10, 85). In what amounts to an unremarked “Temptation,” Severian offers the Claw of the Conciliator to Vodalus. Vodalus proves to be afraid of the Claw, saying, “If I were to possess it, they [the rabble] would think me a desecrator and an enemy of the Theologoumenon. Our masters would think me turned traitor” (85). In this, Vodalus seems to be using the term as a synonym for the Conciliator himself.
Bible: A “theologoumenon” is a theological statement or concept that lacks absolute doctrinal authority. The Catholic idea of Limbo is an example, once a widespread concept now generally abandoned. So one reading has Vodalus saying that the belief in the Conciliator is a popular yet baseless religion.
(Yet applying the term to an individual or a relic seems to be unusual.)
The term shows up two more times in Severian's narrative.
(III, chap. 28) “The columns of the carapace would then be the armies of the Theologoumenon, terrible and gleaming...” This line provides some triangulation, in that Severian uses the term, so it is not limited to Vodalus and his particular bundle of positions.
(IV, chap. 14) “I came forward and knelt before it. I needed no scholar to tell me the Theologoumenon was no nearer now. Yet he seemed nearer...” This line further reinforces that the term is about the person of the Conciliator himself, rather than being about casting doubt upon the relic, or something else like that.
I should amend the “one reading” line above into “So one reading has Vodalus saying that the belief in the Conciliator is a popular religion not directly supported by scripture,” since, as I understand it, “theologoumenon” is about pious belief or individual opinion that cannot be substantiated. My using the word “baseless” makes it seem as though theologoumenon is only applied to discarded or discredited ideas. I only used the case of “Limbo” above to avoid sensitivities to more active theologoumenons such as the virginity of Mary, or the necessity that the messiah had to be born in Bethlehem.
This being Wolfe, it is possible that he is using the term in its original Greek meaning as “that which is said about God,” but this seems even more difficult when applied to a person.