archaia in Ignatius

Ignatius, bishop of Antioch in the early second century CE who was marched to Rome and (presumably) martyred, records an interesting encounter with some of his opponents:

I heard of some people who said, "Unless I find it in the archives, I do not believe it in the gospel. When I told them, "It is written," they replied, "That is the question." But for me the archives are Jesus Christ; the sacred archives are his cross, his death, and his resurrection, and the faith that is granted through him.

ἤκουσά τινων λεγόντων ὅτι Ἐὰν μὴ ἐν τοῖς ἀρχείοις εὕρω, ἐν τῷ εὐαγγελίῳ οὐ πιστεύω· καὶ λέγοντός μου αὐτοῖς ὅτι Γέγραπται, ἀπεκρίθησάν μοι ὅτι Πρόκειται. ἐμοὶ δὲ ἀρχεῖά ἐστιν Ἰησοῦς Χριστός, τὰ ἄθικτα ἀρχεῖα ὁ σταυρὸς αὐτοῦ καὶ ὁ θάνατος καὶ ἡ ἀνάστασις αὐτοῦ καὶ ἡ πίστις ἡ δι ̓ αὐτοῦ· (Ign. Phil. 8.2)

In his chapter on "Early Christian Libraries" (144–2202), Harry Gamble offers the following discussion of the critical word, "archives" [ἀρχεῖα; archeia]:

The sense of this anecdote has been much debated, but what is important for my purposes is the meaning of the term archeion. Its original sense is "governmental house" or "magistrate's office," whence it came to mean "records office" and could signify either the place where records were kept or the records themselves. Most commentators take the word to mean "the original records" and to refer to the Jewish scriptures regarded as "archival records" or "charter documents" of the church. This is surely correct but does not necessarily exhaust the sense of this unique designation of Jewish scripture, for the word alludes to the place where such writings were deposited and available. Since its use by Ignatius's opponents has no clear ulterior motivation, all the more may it imply the existence of an archive or library of the Antiochene church where the Jewish scriptures, among other documents, were kept. (Books and Readers in the Early Church: A History of Early Christian Texts [New Haven and London: Yale University Press, 1995], 152–53)