The sixth ^3-^8 often seems more comfortably regarded as a transformation of ^1-^3 through INVersion or ADDINV (in the first case, the sixth replaces the third; in the second case, the sixth is added onto the third).
In D779n13, however, the prominent sixth ^3-^8 of the closing cadence is unavoidable; it generates a foil to the previous reading's static ^3-^5: the new reading is the most sharply teleological of the nine, as everything must be read "backwards" from the voicing of the final right-hand chord.
In the graphic below, the proto-background is at the top. The second level shows the distribution of the pitches over the form (A5 appears at the end of the first strain), along with the first elaboration by means of neighbor notes (as N-1 in both voices). The third level shows the origins of the C# major section in a temporally displaced (and registrally elaborated) INV transformation. The material below the third level shows later iterations of the same kind of registral play with the basic pitch classes.
For other examples of the ^3-^8 proto-background, see my web essays [NOTE 10 June 2016: both essays named here have been integrated into my PDF essay Proto-backgrounds in Traditional Tonal Music: link] on Beethoven WoO10n2, where ^3-^8, curiously, plays the anti-teleological role among the several readings; and Beethoven WoO10n1, in which registral shifts upward elaborate a neighbor-note pair (no commentary).
