Wolfe's PE revelation that Thecla's "fourth book" = TBOTNS is just so unconvincing on internal grounds. It's obviously ludicrous from a narrative perspective, if it refers to our TBOTNS; and it doesn't make a whole lot more sense if it refers to Canog's (why doesn't he cite it rather than Talos' play as the source of his jail-cell sermon in UOTNS - and so on.)
Pretending this annoying revelation never happened: Is there any internal evidence for what the fourth book might have been?
Apologies if this is repeating Old Stuff, but I hadn't really noticed the following passage before, near the beginning of Ch X of Shadow:
"The books I had carried to her became my university ... If educated men have sometimes thought me ... one whose company did not shame them, that is owing solely to Thecla ... and the four books. ... Thecla ... delighted in talking to me [A] of the secrets of the past, [B] of the conjectures formed of higher spheres and [C] of the arms and histories of heroes millennia dead."
Presumably [A] refers to the Brown Book, and [B] to the smallest, green book. What does [C] refer to? Assuming it doesn't also refer to the Brown Book (which maybe you could argue), I guess it must be either the large, saffian book or the fourth book.
The saffian book is, we are told, a book of heraldry. Would such a book also tell of the "arms and histories of heroes millenia dead"? Maybe, I suppose, but in the absence of anything else I'd tend to assume something focused on lineage and the quarterings of coats of arms etc, without a great deal of history. Just after the quoted passage, Sev refers to Thecla & he "tracing the lineage of old houses", which I assume refers to the saffian book. Does this constitute a [D] to be added to the list, leaving [C] for the "fourth book"?
If so, then my internal guess at the contents of the fourth book might have been something like an epic poem - "arma virumque cano". What would I do with this? Well, I think we're safe in assuming that Thecla is to some extent a follower of Vodalus. His agenda is "return to ancient glory" which I think has to mean: "return to the time when exultants were in charge, before the time of the Autarchs." But I think Thecla also has ambitions beyond those of a follower.
The fourth book might be the Iliad or Aeneid of the exultants, both a the source-text for the "ancient glory", and the normal kind of legend cycle by which an elite group establishes its hierarchy of prestige: trace a direct lineage back to an ancestral hero, and you have juice. Requesting the saffian book & the lineage tracing would be her attempts to do this for herself. The Brown Book would be a source of further material for building up the Thecla-ancestry- legend, and the theology book would give ideas for how to dress it up with a mantle of divine accreditation, for the masses (I think in this Byzantine society, the ruler would always need to be a priest-king to some extant).
Thecla wants to be Autarch, maybe as consort, maybe in her own right. (She has grown up with the prophecy that she would sit a throne; she talks of forging a new religion; the irony of her fate is blatant.) Maybe she is driven partly by jealousy of Thea.
She's not single minded about this ambition; she also talks of retiring to the country and so on. Thea is, I think, the steely one; Thecla is a bit of a ditz.
Anyway, something along those lines works for me better than the story we're apparently supposed to believe :)